CBSE Class 9 Maths Surface Areas and Volumes MCQs

Question: Each side of a cube is increased by 50%. Then the surface area of the cube increases by
a) 50%
b) 100%
c) 150%
d) 125%

Answer: 50%

Question: Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal and saved a distance equal to half the longer side. Then the ratio of the shorter side to the longer side is
a) 3/4
b) 2/3
c) 1/2
d) 1/4

Answer: 3/4

Question: The number of surfaces in right circular cylinder is
a) 4
b) 2
c) 1
d) 3

Answer: 4

Question: A covered wooden box has the inner measures as 115 cm, 75 cm and 35 cm. Find the volume of the wood.
a) 82,125 cu cm
b) 85,000 cu cm
c) 84,000 cu cm
d) 80,000 cu cm

Answer: 82,125 cu cm

Question: The edge of a cube is 20 cm. How many small cubes of 5 cm edge can be formed from this cube?
a) 64
b) 4
c) 32
d) 100

Answer: 64

Question: A metallic right circular cone of height 9 cm and base radius 7 cm is melted into a cuboid whose two sides are 11 cm and 6 cm. What is the third side of the cuboid?
a) 7 cm
b) 5 cm
c) 6 cm
d) 10 cm

Answer: 7 cm

Question: The slant height of a cone is increased by P%. If radius remains same, the curved surface area is increased by
a) P%
b) 2P%
c) P²%
d) None of these

Answer: P%

Question: The dimensions of a hall are 40 m, 25 m and 20 m. if each person requires 200 cubic metre, then the number of persons who can be accommodated in the hall are
a) 100
b) 150
c) 120
d) 140

Answer: 100

Question: A hollow spherical ball whose inner radius is 4 cm is full of water. Half of the water is transferred to a conical cup and it completely filled the cup. If the height of the cup is 2 cm, then the radius of the base of cone, in cm is
a) 8
b) 4
c) 16
d) 12

Answer: 8

Question: The radius of the cylinder whose lateral surface area is 704 cm² and height 8 cm is
a) 14 cm
b) 4 cm
c) 6 cm
d) 8 cm

Answer: 14 cm

Question: The radius of cylinder is doubled but its lateral surface area is unchanged. Then its height must be
a) halved
b) constant
c) doubled
d) tribled

Answer: halved

Question: The ratio of the volume and surface area of a sphere of unit radius
a) 1 : 3
b) 4 : 3
c) 3 : 4
d) 3 : 1

Answer: 1 : 3

Question: A cylindrical rod whose height is 8 times of its radius is melted and recast into spherical balls of same radius. The number of balls will be
a) 6
b) 4
c) 3
d) 8

Answer: 6

Question: A sphere and a cube are of the same height. The ratio of their volume is
a) 11 : 21
b) 21 : 11
c) 3 : 4
d) 4 : 3

Answer: 11 : 21

Question. The surface area of a cuboid is
(a) 2(lb + bh + lh)
(b) 3(lb + bh + lh)
(c) 2(lb – bh – lh)
(d) 3(lb – bh – lh)

Question. The surface area of a cube if edge ‘a’ is
(a) 7a²
(b) 6a²
(c) 5a³
(d) 5a²

Question. The length, breadth and height of a room is 5m, 4m and 3m. The cost of white washing its four walls at the rate of Rs. 7.50 per m² is
(a) Rs. 110
(b) Rs. 109
(c) Rs. 220
(d) Rs. 105

Question. The perimeter of floor of rectangular hall is 250m. The cost of the white washing its four walls is Rs. 15000. The height of the room is
(a) 5m
(b) 4m
(c) 6m
(d) 8m

Question. The breadth of a room is twice its height and is half of its length. The volume of room is 512dm³. Its dimensions are
(a) 16 dm, 8 dm, 4 dm
(b) 12 dm, 8 dm, 2 dm
(c) 8 dm, 4 dm, 2 dm
(d) 10 dm, 15 dm, 20 dm

Question. The area of three adjacent faces of a cube is x, y and z. Its volume V is
(a) V = xyz
(b) V³ = xyz
(c) V² = xyz
(d) none of these

Question. Two cubes each of edge 12 cm are joined. The surface area of new cuboid is
(a) 140 cm²
(b) 1440 cm²  
(c) 144 cm² 
(d) 72 cm² 

Question. The curved surface area of cylinder of height ‘h’ and base radius ‘r’ is
(a) 2∏rh
(b) ∏rh
(c) 1/2∏rh
(d) none of these

Question. The total surface area of cylinder of base radius ‘r’ and height ‘h’ is
(a) 2π(r + h)
(b) 2πr(r + h)
(c) 3πr(r + h)
(d) 4πr(r + h)

Question. The curved surface area of a cylinder of height 14 cm is 88 cm². The diameter of its circular base is
(a) 5cm
(b) 4cm
(c) 3cm
(d) 2cm

Question. It is required to make a closed cylindrical tank of height 1 m and base diameter 140cm from a metal sheet. How many square meters a sheet are required for the same?
(a) 6.45m²
(b) 6.48m²
(c) 7.48m²
(d) 5.48m².

Question. A metal pipe is 77 cm long. Inner diameter of cross section is 4 cm and outer diameter is 4.4 cm. Its inner curved surface area is:
(a) 864 cm²
(b) 968 cm²
(c) 768 cm²
(d) none of these

Question: Vertical and horizontal cross-sections of a right circular cylinder are always respectively

Question. A joker’s cap is in the form of cone of base radius 7 cm and height 24 cm. The area of sheet to make 10 such caps is
(a) 5500 cm²
(b) 6500 cm²
(c) 8500 cm²
(d) 3500 cm²

Question. The curved surface area of a hemisphere of radius ‘r’ is
(a) 2∏r²
(b) 4∏r²
(c) 3∏r²
(d) 5∏r²

Question. The total surface area of a hemisphere of radius ‘r’ is
(a) 2∏r²
(b) 4∏r²
(c) 3∏r²
(d) 5∏r²

Question. The curved surface area of a sphere of radius 7 cm is:
(a) 516 cm²
(b) 616 cm²
(c) 716 cm²
(d) 880 cm²

Question. The curved surface area of a hemisphere of radius 21 cm is:
(a) 2772 cm²
(b) 2564 cm²
(c) 3772 cm²
(d) 4772 cm²

Question. The curved surface area of a sphere of radius 14 cm is:
(a) 2464 cm²
(b) 2428 cm²
(c) 2464 cm²
(d) none of these.

Question. The curved surface area of a sphere of diameter 14 cm is:
(a) 516 cm²
(b) 616 cm²
(c) 716 cm²
(d) 880 cm²

Question. Total surface area of hemisphere of radius 10 cm is
(a) 942 cm²
(b) 940 cm²
(c) 842 cm²
(d) 840 cm²

Question. The radius of a spherical balloon increases from 7 cm to 14 cm s air is being pumped into it. The ratio of surface area of the balloon in the two cases is:
(a) 4 : 1
(b) 1 : 4
(c) 3 : 1
(d) 1 : 3

Question. A matchbox measures 4 cm x 2.5 cm x 1.5 cm. The volume of packet containing 12 such boxes is:
(a) 160 cm³
(b) 180 cm³
(c) 160 cm²
(d) 180 cm²

Question. A cuboidal water tank is 6 m long, 5 m wide and 4.5 m deep. How many litre of water can it hold?
(a) 1350 liters
(b) 13500 liters
(c) 135000 liters
(d) 135 liters

Question. A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of a liquid?
(a) 4.75 m
(b) 7.85 m
(c) 4.75 cm
(d) none of these

Question. The capacity of a cuboidal tank is 50000 litres. The length and depth are respectively 2.5 m and 10 m. Its breadth is
(a) 4 m
(b) 3 m
(c) 2 m
(d) 5 m

Question. A godown measures 40 m × 25 m × 10 m. Find the maximum number of wooden crates each measuring 1.5 m × 1.25 m × 0.5 m that can be stored in the godown.
(a) 18000
(b) 16000
(c) 15000
(d) 14000

Question. A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute?
(a) 4000 m³
(b) 40 m³
(c) 400 m³
(d) 40000 m³

Question. The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. How many litres of water can it hold?
(a) 33.75 litre
(b) 34.65 litre
(c) 35.75 litre
(d) 38.75 litre

Question. If the lateral surface of a cylinder is 94.2 cm² and its height is 5 cm, then find radius of its base
(a) 5cm
(b) 4cm
(c) 3cm
(d) 6cm

Question. It costs Rs 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of Rs 20 per m2, find radius of the base,
(a) 1.75 m
(b) 1.85 m
(c) 1.95 m
(d) 1.65 m

Question. The height and the slant height of a cone are 21 cm and 28 cm respectively. Find the volume of the cone.
(a) 5546 cm³
(b) 7546 cm³
(c) 5564 m³
(d) 8546 cm³

Question. Find the volume of the right circular cone with radius 6 cm, height 7 cm
(a) 254 cm³
(b) 264 cm³
(c) 274 cm²
(d) 284 cm³

Question. The radius and height of a conical vessel are 7 cm and 25 cm respectively. Its capacity in litres is
(a) 1.232 litre
(b) 1.5 litre
(c) 1.35 litre
(d) 1.6 litre

Question. The height of a cone is 15 cm. If its volume is 1570 cm³, find the radius of the base.
(a) 12 cm
(b) 10 cm
(c) 15 cm
(d) 18 cm

Question. If the volume of a right circular cone of height 9 cm is 48π cm³, find the diameter of its base.
(a) 12 cm
(b) 10 cm
(c) 6 cm
(d) 8 cm

Question. A conical pit of top diameter 3.5 m is 12 m deep. What is its capacity in kilolitres?
(a) 38.5 kl
(b) 48.5 kl
(c) 39.5 kl
(d) 47.5 kl

Question. Find the capacity in litres of a conical vessel with radius 7 cm, slant height 25 cm
(a) 1.232 litre
(b) 1.5 litre
(c) 1.35 litre
(d) none of these

Question. The diameter of the moon is approximately one-fourth of the diameter of the earth. What fraction of the volume of the earth is the volume of the moon?
(a) 1/64 
(b) 1/ 32   
(c) 1/16 
(d) 1/48

Question. The dimensions of a cuboid are 50 cm x 40 cm x 10 cm. Its volume in litres is:
(a) 10 litres
(b) 12 litres
(c) 20 litres
(d) 25 litres

Question. The volume of a cuboidal tank is 250 m³. If its base area is 50 m² then depth of the tank is
(a) 5 m
(b) 200 m
(c) 300 m
(d) 12500 m

Question. The length, breadth and height of a cuboidal solid is 4 cm, 3 cm and 2 cm respectively. Its volume is
(a) (4 + 3 +2) cm³
(b) 2(4 + 3 +2) cm³
(c) (4 x 3 x 2) cm³
(d) 2(4 + 3) x 2 cm³

Question. The volume of a cuboidal solid of length 8 m and breadth 5 m is 200 m³. Find its height.
(a) 5 m
(b) 6 m
(c) 15 m
(d) 18 m

Question. The curved surface area of a sphere is 616 cm². Its radius is
(a) 7 cm
(b) 5 cm
(c) 6 cm
(d) 8 cm

Question. If radius of a sphere is 2d/3 then its volume is
(a) 32/81πd³
(b) 23/4πd³
(c) 32/3πd³
(d) 34/3πd³

Question. The capacity of a cylindrical tank is 6160 cm³. Its base diameter is 28 m. The depth of this tank is
(a) 5 m
(b) 10 m
(c) 15 m
(d) 8 m

Question. The volume of a cylinder of radius r and length h is:
(a) 2πrh
(b) 4/3πr²h
(c) πr²h
(d) 2πr²h

Question. Base radius of two cylinder are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. The ratio of their volumes is
(a) 27 : 20
(b) 25 : 24
(c) 20 : 27
(d) 15 : 20

Question. If base radius and height of a cylinder are increased by 100% then its volume increased by:
(a) 30%
(b) 40%
(c) 42%
(d) 33.1%

Question. The diameter of a sphere is 14 m. The volume of this sphere is 
(a) 1437 1/3 m³
(b) 1357 1/3 m³
(c) 1437 2/3 m³
(d) 1337 2/3 m³

Question. The volume of a sphere is 524 cm3. The diameter of sphere is
(a) 5cm
(b) 4cm
(c) 3cm
(d) 7cm

Question. The total surface area of a cylinder is 40π cm². If height is 5.5 cm then its base radius is
(a) 5cm
(b) 2.5cm
(c) 1.5cm
(d) 10cm

Question. The area of circular base of a right circular cone is 78.5 cm². If its height is 12 cm then its volume is
(a) 31.4 cm³
(b) 3.14 cm³
(c) 314 cm³
(d) none of these

Question. The base radius of a cone is 11.3 cm and curved surface area is 355 cm². Its height is (Take π = 355/113)
(a) 5 cm
(b) 10 cm
(c) 11 cm
(d) 9 cm

1. The space occupied by a solid body is called its volume. The units of volume are cubic centimetre (cm³) or cubic metres (m³) etc.

2. Cuboid : A solid bounded by six rectangular plane faces is called a cuboid.

3. Cube : A cuboid whose length, breadth and height are all equal is called a cube.

4. Cuboid : For a cuboid of length = l units, breadth = b units and height = h units.
(i) Volume of cuboid = (l × b × h) cubic units
(ii) Diagonal of the cuboid = √l² + b² + h² units
(iii) Total surface area of the cuboid = 2(lb + bh + lh) sq units
(iv) Lateral surface area of the cuboid = [2(l + b) × h] sq units
(v) Area of 4 walls of a room = [2(l + b) × h] sq units

5. Cube : For a cube of edge = a units
(i) Volume of the cube = a3 cubic units
(ii) Diagonal of the cube = a √3 units
(iii) Total surface area of the cube = (6a²) sq units
(iv) Lateral surface are of the cube = (4a²) sq units
Relation between units
Length units Volume units
1 cm = 10 mm 1 cm² = 1000 mm³
100 cm = 1 m 1 m³ = 1000000 cm³
1 litre = 1000 cm³
1 kilolitre = 1000 litres = 1 m³

6. Cylinder : A solid having a curved surface as a lateral surface and a uniform circular cross-section is known as a cylinder

b If the axis of the cylinder is perpendicular to each cross-section then the cylinder is called a right circular cylinder

7. Volume of a cylinder : For a cylinder whose height is a h units and the radius of whose base is r units, Volume of cylinder = (πr²h) cubic units = (base area) × height

8. Surface area of cylinder : For a cylinder of height h and radius r :
(a) Area of curved surface = (2 πrh) sq units
(b) Total surface area = (2πrh + 2π r²) sq units

9. Cone : It is a solid having a plane circular end as the base and whose lateral surface is a curved surface tapering into a point, called its vertex. 

Note : For a right circular cone, we have AO is perpendicular to OB, i.e., ΔAOB is right angled at O. Hence, l² = r² + h²

10. Volume of a cone : For a cone of radius r units and height h units, volume of cone = (1/3 πr²h) cubic units.

11. Area of curved surface : For a cone of radius r, height h and slant height l,
(a) Area of curved surface = prl sq units
(b) Total surface area = (πrl + πr2) sq units

12. (a) Sphere : The set of all points in space equidistant from a fixed point is called a sphere.
(b) Hemisphere : A plane through the centre of a sphere cuts it into two equal parts. Each part is called a hemisphere.
(c) Spherical shell : The difference of two solid concentric spheres is called a spherical shell. 

13. For a sphere of radius r units : 
(a) Volume of sphere = (1/3πr³) cubic units
(b) Area of curved surface of the sphere = (4πr²) cubic units
(c) Volume of the hemisphere = (1/3πr3)cubic units
(d) Curved surface of the hemisphere = (2πr²) sq units
(e) Total surface area of the hemisphere = 2πr² + πr² = (3πr²) sq units

Question. A cooking pot has a spherical bottom, while the upper part is a truncated cone. Its vertical crosssection is shown in the figure. If the volume of food increases by 15% during cooking, the maximum initial volume of food that can be cooked without spilling is (in cc) 

(A) 14450 π/3
(B) 19550  π/3
(C) 340000/69π
(D) 20000/3 π

Answer: D

Question. Each side of a cube is increased by 50%. Then the surface area of the cube increases by
(A) 50%
(B) 100%
(C) 125%
(D) 150%

Answer: C

Question. Three cylinders each of height 16 cm and radius of base 4 cm are placed on a plane so that each cylinder touches the other two. Then the volume of region enclosed between the three cylinders in cm³ is
(A) 98(4 √3 - π)
(B) 98(2 √3 - π)
(C) 98( √3 - π)
(D) 128(2 √3 - π)

Answer: D

Question. Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal and saved a distance equal to half the longer side. Then the ratio of the shorter side to the longer side is
(A) 1/2
(B) 2/3
(C) 1/4
(D) 3/4

Answer: D

Question. The number of surfaces in right circular cylinder is 
(A) 1
(B) 2
(C) 3
(D) 4

Answer: C

Question. 

Fields X and Y are to be enclosed with a fencing at the cost of Rs 40 per meter. If the cost on field X is denoted by Cx and that on field Y is denoted by Cy we have 
(A) C_x = C_y
(B) C_x < C_y
(C) C_x > C_y
(D) cannot be determined 

Answer: A

Question. A covered wooden box has the inner measures as 115 cm, 75 cm and 35 cm. Find the volume of the wood.
(A) 80,000 cu cm
(B) 82,125 cu cm
(C) 84,000 cu cm
(D) 85,000 cu cm

Answer: B

Question. The edge of a cube is 20 cm. How many small cubes of 5 cm edge can be formed from this cube?
(A) 4
(B) 32
(C) 64
(D) 100

Answer: C

Question. Two cylinders of same volume have their heights in the ratio 1 : 3. Find the ratio of their radii.
(A) √3 :1
(B) √2 :1
(C) √5 : 2
(D) 2: √5

Answer: A

Question. A metallic right circular cone of height 9 cm and base radius 7 cm is melted into a cuboid whose two sides are 11 cm and 6 cm. What is the third side of the cuboid?
(A) 5 cm
(B) 6 cm
(C) 7 cm
(D) 10 cm

Answer: C

Question. The slant height of a cone is increased by P%. If radius remains same, the curved surface area is increased by
(A) P%
(B) P2%
(C) 2P%
(D) None

Answer: A

Question. The volumes of two spheres are in the ration 64 : 27. Find the difference of their surface areas, if the sum of their radii is 7 units
(A) 28π sq units
(B) 88 sq units
(C) 88π sq units
(D) 4π sq units

Answer: A

Question. In the figure below, LMNO and GHJK are rectangles where GH = 1/2 LM and HJ = 1/2 MN. What fraction of the region is bounded by LMNO that is not shaded?
(A) 1/4
(B) 1/3
(C) 1/2
(D) 3/4

Answer: D

Question. In the figure below, RSTV is a square inscribed in a circle with centre O and radius r. The total are of shaded region is
(A) r²(π – 2)
(B) 2r(2 – π)
(C) π(r² – 2)
(D) π r² – 8r 

Answer: A

Question. A right circular cone of diameter K cm and height 12 cm rests on the base of a right circular cylinder of radius K cm (their bases lie in the same plane, as shown in figure). The cylinder is filled with water to a height of 12 cm. If the cone is then removed, the height to which water will fall is 

(A) 11 cm
(B) 10 cm
(C) 8 cm
(D) cannot be determined from given data

Answer: A

Question. The ratio of radii of two cylinders is 1 : √3 and heights are in the ratio 2 : 3. The ratio of their volumes is
(A) 1 : 9
(B) 2 : 9
(C) 4 : 9
(D) 5 : 9

Answer: B

Question. The dimensions of a hall are 40 m, 25 m and 20 m. if each person requires 200 cubic metre, then the number of persons who can be accommodated in the hall are
(A) 120
(B) 150
(C) 140
(D) 100

Answer: D

Question. Correct the perimeter of the figure given below to one decimal place. 

(A) 56.0 m
(B) 56.6 m
(C) 57.2 m
(D) 57.9 m

Answer: B

Question. A hollow spherical ball whose inner radius is 4 cm is full of water. Half of the water is transferred to a conical cup and it completely filled the cup. If the height of the cup is 2 cm, then the radius of the base of cone, in cm is
(A) 4
(B) 8π
(C) 8
(D) 16

Answer: C

Question. The largest volume of cube that can be inclosed in a sphere of diameter 2 cm is (in cm³)
(A) 1
(B) 2 √2
(C) π
(D) 8/3√3

Answer: B

Question. The radius of the cylinder whose lateral surface area is 704 cm² and height 8 cm is
(A) 6 cm
(B) 4 cm
(C) 8 cm
(D) 14 cm

Answer: D

Question. The radius of a sphere is increased by P%. Its surface area increases by
(A) P%
(B) P2%
(C) 8(2P+P²/100)%
(D) P²/P %

Answer: C

Question. The radius of cylinder is doubled but its lateral surface area is unchanged. Then its height must be
(A) doubled
(B) halved
(C) tribled
(D) constant

Answer: B

Question. The height and radius of a cone are 3 cm and 4 cm respectively. Its curved surface area must be is
(A) 62x 6/7 sq cm
(B) 57x 3/4 sq cm
(C) 6 cm²
(D) 12 cm²

Answer: A

Question. The ratio of the volume and surface area of a sphere of unit radius
(A) 4 : 3
(B) 3 : 4
(C) 1 : 3
(D) 3 : 1

Answer: C

Question. A cylindrical rod whose height is 8 times of its radius is melted and recast into spherical balls of same radius. The number of balls will be
(A) 4
(B) 3
(C) 6
(D) 8

Answer: C

Question. Two identical right circular cones each of height 2 cm are placed as shown in diagram (each is vertical, apex downward). At the start, the upper cone is full of water and lower cone is empty.
Then water drips down through a hole in the apex of upper cone into the lower cone. The height of water in the lower cone at the moment when height of water in upper cone is 1 cm is

Answer: D

Question. A sphere and a cube are of the same height. The ratio of their volume is
(A) 3 : 4
(B) 21 : 11
(C) 4 : 3
(D) 11 : 21

Answer: D

Question. The largest sphere is cut off from a cube of side 5 cm. The volume of the sphere will be
(A) 27 π cm³
(B) 30 π cm³
(C) 108 π cm²
(D) 125 π/6 cm³

Answer: D

Question. Vertical and horizontal cross-sections of a right circular cylinder are always respectively
(A) rectangle, square
(B) rectangle, circle
(C) square, circle
(D) rectangle, ellipse

Answer: B

Question. A right cylindrical vessel is full with water. How many right cones having same diameter and height as of right cylinder will be needed to store that water?
(A) 2
(B) 4
(C) 3
(D) 5

Answer: C

Question. Two cylinders of same volume have their heights in the ration 1 : 3. Then the ratio of their radii is
(A) √3 :1
(B) √2 :1
(C) √5 : 2
(D) 2: v5

Answer: A

Question. ABC is a right angled triangle with ∠ABC = 90º . AH is drawn perpendicular to BC where H lies on BC. If AB = 60 cm and AC = 80 cm, then BH =

(A) 36 cm
(B) 32 cm
(C) 24 cm
(D) 30 cm

Answer: A

Question. The area of a trapezium is 28 cm2 and one of its parallel sides 6 cm. If its altitude is 4 cm., then its other parallel side is
(A) 8 cm
(B) 4 cm
(C) 6 cm
(D) 9 cm

Answer: A

Question. The area of the union of all squares with side 1 cm whose centre lies on a fixed square with side 1 cm euqals
(A) (3+π/4) cm³
(B) (π/2 + 2√2 + 1) cm²
(C) (7/2) cm²
(D) (2√2 + 2)cm²

Answer: B

Question. If the area of a triangle with base x is equal to area of a square of side x, the altitude of the triangle is
(A) x/2
(B) x
(C) √2x
(D) 2x

Answer: A

Question. The ratio of the areas of a square to that of a square drawn on its diagonal is
(A) 1 : 1
(B) 1 : 2
(C) 1 : 3
(D) 1 : 4

Answer: B

Question. A man bought a rectangle plot of 144 m length and 64 m width. In exchange for this field he wanted to buy a square field of the same area. Then the side of the square field would be
(A) 104 m
(B) 208 m
(C) 96 m
(D) 406 m

Answer: C

Question. A metal sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. The difference between surface areas of two solids is
(A) 284 cm²
(B) 286 cm²
(C) 296 cm²
(D) 280 cm²

Answer: B

Question. Three cubes whose edges are 3 cm, 4 cm and 5 cm respectively are melted without any loss of metal into a single cube. The edge of new cube is
(A) 6 cm
(B) 12 cm
(C) 9 cm
(D) 10 cm

Answer: A

Question. If length, breadth and height of rectangular parallelopiped are in ratio 6 : 5 : 4 and total surface area is 33,300 m2, then length breadth and height of parallelopiped are in (m)
(A) 90, 75 , 70
(B) 85, 75, 60
(C) 90, 75, 60
(D) 80, 70, 60

Answer: C

Question. The radius of the cylinder whose lateral surface area is 704 cm23 and height 8 cm, is
(A) 6 cm
(B) 4 cm
(C) 8 cm
(D) 14 cm

Answer: D

Question. A covered wooden box has the inner measures as 115 cm, 75 cm and 35 cm and the thickness of wood is 2.5 cm. The volume of the wood, is
(A) 80,000 cu cm
(B) 82,125 cu cm
(C) 84,000 cu cm
(D) 85,000 cu cm

Answer: B

Question. Four circles of equal radii are centred at the four vertices of a square. These 4 circles touch a fifth circle of equal radius placed inside the square. The ratio of the shaded area of the circles to the unshaded area of the circles is 

(A) 1 : 3
(B) 2 : 3
(C) 3 : 4
(D) 2 : 5

Answer: B

Question. The ratio of radii of two cylinders is 1: √3 and heights are in the ratio 2 : 3 The ratio of their volume is
(A) 1 : 9
(B) 2 : 9
(C) 4 : 9
(D) 5 : 9

Answer: B

Question. A solid cube is chopped off at each of its 8 corners to create an equilateral triangle with 3 new corners. The 24 corners are now joined to each other by diagonals. How many of these diagonals completely lie inside the cube?
(A) 120
(B) 108
(C) 96
(D) 100

Answer: A

Question. Two cubes have volume in the ratio 1 : 27. The ratio of the area of the face of one to that of the other is
(A) 1 : 3
(B) 1 : 6
(C) 1 : 9
(D) 1 : 18

Answer: C

Question. The surface areas of the six faces of a rectangular solid are 4, 4, 8, 8, 18 and 18 square centimetres.
The volume of the solid, in cubic centimetres is
(A) 24
(B) 48
(C) 60
(D) 324

Answer: A

Question. Instead of waling along two adjacent sides of rectangular field, a boy took a short cut along the diagonal and saved a distance equal to half the longer side. Then the ratio of the shorter side to the longer side, is
(A) 1/2
(B) 2/3
(C) 1/4
(D) 3/4

Answer: D

Question. A rectangle field has its length and breadth in the ratio 5 : 3. Its area is 3.75 hectares. The cost of fencing it at Rs. 5 per meter is
(A) Rs. 400
(B) Rs. 4000
(C) Rs. 1000
(D) Rs. 500

Answer: B

Question. Two rectangles ABCD and DBEF are as shown in the figure. The area of rectangle DBEF in square units is 

(A) 10
(B) 12
(C) 14
(D) 15

Answer: B

Question. The diagonals of a rhombus are 7.5 cm and 12 cm. Then the area of rhombus is
(A) 45 cm²
(B) 90 cm²
(C) 22.5 cm²
(D) 180 cm²

Answer: A

Question. How many diagonals does a 12 - sided regular polygon have?
(A) 35
(B) 50
(C) 54
(D) 30

Answer: C

Question. What change in percent is made in the area of a rectangle by decreasing its length and increasing its breadth by 5%?
(A) 2.5% increase
(B) 0.25 % increase
(C) 0.25% decrease
(D) 2.5 % decrease

Answer: B

Question. The ratio of areas of two squares, one having double its diagonal than the other is
(A) 3 : 2
(B) 4 : 1
(C) 3 : 1
(D) 4 : 3

Answer: C

Question. A child walked 5 m to cross a rectangular field diagonally. If breadth of field is 3 m, its length is
(A) 4 m
(B) 3 m
(C) 10 m
(D) 6 m

Answer: A

Question. The length of longest rod that can fit in a cubical room of 4 m side is
(A) 8.66 m
(B) 5.196 m
(C) 6.928 m
(D) 5 m

Answer: C

Question. The area of a rhombus is 28 cm² and one of its diagonals is 4 cm. Its perimeter is
(A) 4 √53 m
(B) 36 cm
(B) 2 √53 m
(D) None of these

Answer: A

Question. The adjacent sides of a parallelogram are 8 cm and 9 cm. The diagonal joining the ends of these sides is 13 cm. Its area is
(A) 72 cm²
(B) 12 35 cm²
(C) 24 35 cm²
(D) 150 cm²

Answer: B

Question. The number of surfaces in right circular cylinder, is
(A) 1
(B) 2
(C) 3
(D) 4

Answer: C

Question. A square pond has 2 m sides and is 1 m deep. If it is to be enlarged, the depth remaining the same, into a circular pond with the diagonal of the square as diameter as shown in the figure, the what would be the volume of earth to be removed ? 

(A) (2π – 4) m³
(B) (4π – 4) m³
(C) (4π – 2) m³
(D) (2π – 2) m³

Answer: A

Question. Two circular cylinders of equal volume have heights in the ratio of 1 “ 2. The ratio of their radii is
(A) 1 : 2
(B) 2 : 1
(C) 1: √2
(D) √2 :1

Answer: D

Question. A rectangle ground is 90 m long and 32 m broad. In the middle of the ground there is a circular tank of radius 14 meters. The cost of turfing the remaining portion at the rate of Rs. 2.50 per square meter is
(A) Rs. 6000
(B) Rs. 5660
(C) Rs. 5800
(D) Rs. 5750

Answer: B

Question. If the diagonal of a square is doubled, the area of the square becomes
(A) 2 times
(B) 3 times
(C) 4 times
(D) 6 times

Answer: C

Question. The area of the field if M is the mid point of LN is 

(A) 15200 sq. units
(B) 13300 sq. units
(C) 15000 sq. units
(D) 27800 sq. units

Answer: B

Question. The area of the trapezium ABCD as shown in the figure (in square units) is 

(A) 222
(B) 111
(C) 224
(D) 116

Answer: A

Question. What is the length of AC? (All dimensions are in cm) 

(A) 95
(B) 75
(C) 85
(D) 65

Answer: D

Question. What is the volume of the rectangular solid shown below ? 

(A) 520 cm³
(B) 725 cm³
(C) 420 cm³
(D) 720 cm³

Answer: D

Question. The hypotenuse of a triangle is 29 cm and one of its sides is 20 cm, then the other side is
(A) 20 cm
(B) 21 cm
(C) 27 cm
(D) 25 cm

Answer: B

Question. A hoop is resting vertically at stair case as shown in the diagram. AB = 12 cm and BC = 8 cm. The radius of the hoop is 

(A) 13 cm
(B) 12 √2 cm
(C) 14 cm
(D) 13 √2 cm

Answer: A

Question. O is the centre of the regular pentagon. What part of the whole pentagon is the shaded region ?

(A) 10 %
(B) 20 %
(C) 25 %
(D) 30 %

Answer: D

Question. The perimeter of the figure given below correct to one decimal place is 

(A) 56.0 m
(B) 56.6 m
(C) 57.2 m
(D) 57.9 m

Answer: B

Question. The ratio between the length and the perimeter of a rectangular plot is 1 : 3 and the ratio between the breadth and perimeter of that plot is 1 : 6. What is the ratio between the length and area of that plot ?
(A) 2 : 1
(B) 1 : 6
(C) 1 : 8
(D) Data inadequate

Answer: D

Question. A cylindrical tower is 5 m in diameter and 14 meter high. The cost of white washing its curved surface at 50 paisa per m2 is
(A) Rs. 90
(B) Rs. 97
(C) Rs. 110
(D) Rs. 95

Answer: C

Question. A square garden measuring 8 m on a side is surrounded by a 1 m wide path. What is the area of the path? 

(A) 8 square m
(B) 9 square m
(C) 28 square m
(D) 36 square m

Answer: D

Question. In the figure below, LMNO and GHJK are rectangles where GH = 1/2 LM and HJ = 1/2 MN. What fraction of the region is bounded by LMNO that is not shaded ? 

(A) 1/4
(B) 1/3
(C) 1/2
(D) 3/4

Answer: D

Question. Each side of cube is increased by 50%. Then the surface area of the cube increase by
(A) 50 %
(B) 100 %
(C) 125 %
(D) 150 %

Answer: C

Question. In the figure below, RSTV is a square inscribed in a circle with centre O and radius r. The total area of shaded region is 

(A) r²(π – 2)
(B) 2r²(2 – π)
(C) π(r² – 2)
(D) 8r² – 8r

Answer: A

Question. The length of diagonal of a square whose area is 16900 m² is
(A) 130 m
(B) 130 2 m
(C) 169 m
(D) 144 m

Answer: B

Question. The dimensions of a hall are 40 m, 25 m and 20 m. If each person requires 200 cubic meter, then the number of persons who can be accommodated in the hall are
(A) 120
(B) 150
(C) 140
(D) 100

Answer: D

Question. What is the ratio of the perimeter of the shaded region to the circumference of the circle ?

(A) 3/4
(B) 4+π/4π
(C) 2π/4+π
(D) 4+π/2π

Answer: B

Question. The volume of a cube is 512 cm³. Its surface area is
(A) 64 cm²
(B) 256 cm²
(C) 384 cm²
(D) 512 cm²

Answer: C

Question. In rectangle ABCD, if BC/BE = CD/DF = √3 . If BE = 6 cm and AF = 2 cm, which of the following integers is nearest to the area of the rectangle ABCD in sq. cm. ? 

(A) 130
(B) 150
(C) 170
(D) 190

Answer: B

Question. In an n sides regular polygon the radius of the circum-circle is equal in length to the shortest diagonal, then n is
(A) 6
(B) 8
(C) 12
(D) Such a polygon does not exist

Answer: C

Question. The sum of sides of cube and rectangular parallelopiped are same. The ratio of volume of cube to that of parallelopied is
(A) 1
(B) Less than 1
(C) Greater than 1
(D) None of these

Answer: C

Question. The area of a rhombus is 120 cm2 and its altitude is 10 cm. The length of the rhombus is
(A) 24 cm
(B) 12 cm
(C) 8 cm
(D) 4 cm

Answer: B

Question. A quadrilateral whose one diagonal is 5.5 cm. If the length of altitudes from opposite vertices on the diagonal is 2.5 cm and 1.5 cm, then the area of quadrilateral is
(A) 22 cm²
(B) 11 cm²
(C) 55 cm²
(D) 33 cm²

Answer: B

Question. Vertical and horizontal cross sections of a right circular cylinder are always respectively
(A) rectangle, square
(B) rectangle, circle
(C) square, circle
(D) rectangle, ellipse

Answer: B

Question. The surface area of the cube given, is 

(A) 3.375 cm²
(B) 13.5 cm²
(C) 6.75 cm²
(D) 9 cm²

Answer: B

Question. Bases of four equilateral triangles form a square. Inside the square four circle of radius 5 units are drawn as in the figure. The perimeter of the four cornered star is 

(A) 100
(B) 120
(C) 160
(D) 200

Answer: C

Question. The diameter of the circle in the picture is 10 cm. The perimeter of the region marked in thick line in cms is 

(A) 12
(B) 16
(C) 20
(D) 24

Answer: C

Question. The diagonal of a isosceles trapezium is 16 cm long and marks an angle of 45° 

(A) 64 cm²
(B) 96 cm²
(C) 128 cm²
(D) 256 cm²

Answer: C 

Question. The radius of a cylinder is doubled but its lateral surface area of unchanged. The its height must be
(A) Doubled
(B) Halved
(C) Trebled
(D) Constant

Answer: B

Question. The perimeter of a trapezium is 52 cm and its non-parallel sides are each equal to 10 cm and its altitude is 8 cm. Its area is
(A) 128 cm²
(B) 112 cm²
(C) 118 cm²
(D) 124 cm²

Answer: A

Question. Total area of quadrilateral ABCD is 20 cm² and offsets on BD are 2 cm and 3 cm. The length of BD is

(A) 5 cm
(B) 6 cm
(C) 8 cm
(D) 10 cm

Answer: C

Question. How many small cubes with edges of 10 cm can be just accommodated in a cubical box of 1 m edge?
(A) 10
(B) 100
(C) 1000
(D) 10000

Answer: C

Question. The largest possible square is inscribed in a circle of unit radius. The area of the square in square units is 
(A) 2
(B) π
(C) 2 √2π
(D) 4 √2π

Answer: A

Question. In this scale drawing of a molding, each square represents 1 square inch. What is the area of the molding?

(A) 24 sq. in
(B) 34 sq. in
(C) 35 sq. in
(D) 37 sq. in

Answer: D

Question. The given figure below shows a square inscribed in a larger square. What is the area of the smaller square ? 

(A) 9 square units
(B) 16 square units
(C) 25 square units
(D) 36 square units

Answer: C