CBSE Class 10 Mathematics Surface Areas and Volumes MCQs

MCQ

Question : A cylindrical pencil sharpened at one edge is the combination of
(a) two cylinders
(b) a hemisphere and a cylinder
(c) a cone and a cylinder
(d) frustum of a cone and a cylinder
Answer : C

Question : The curved surface area of glass having radii 3 cm and 4 cm respectively and slant height 10 cm is
(a) 55 cm²
(b) 110 cm²
(c) 220 cm²
(d) 440 cm²
Answer : C

Question : The ratio of the total surface area of a solid hemisphere to the square of its radius is
a) 2𝜋 : 1
b) 3 𝜋: 1
c) 4 𝜋 : 1
d) 1: 4 𝜋
Answer : B

Question : The radius of a sphere is r cm. The sphere is divided into two equal parts. The whole surface area of two parts will be:
a) 8𝜋𝑟²
b) 6𝜋𝑟²
c) 4𝜋𝑟²
d) 3𝜋𝑟²
Answer : B

Question : The surface area of the two spheres are in the ratio 1 : 2. The ratio of their volumes is :
a) √2: 1
b) 1 : 2√2
c) 1 : 8
d) 1 : 4
Answer : B

Question : The radius of a wire is decreased to one third. If the volume remains the same, the length will become
a) 3 times
b) 6 times
c) 9 times
d) 27 times
Answer : C

Question : Two cubes each of volume 8𝑐𝑚3are joined end to end , then the surface area of the resulting cuboid is
a) 80cm²
b) 64cm²
c) 40cm²
d) 8𝑐cm²
Answer : C

Question : If the areas of three adjacent faces of a cuboid are X, Y and Z respectively, then the
volume of cuboid is :
a) XYZ
b) 2XYZ
c) √𝑋𝑌𝑍
d) √2𝑋𝑌𝑍
Answer : C

Question : The ratio of the volumes of two spheres is 8 : 27 . If r and R are the radii of spheres respectively then (R – r) : r is :
a) 1 : 2
b) 1 : 3
c) 2 : 3
d) 4 : 9
Answer : A

Question : The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3.
Ratio of their volumes is
a) 27 : 20
b) 20 : 27
c) 9: 4
d) 4 : 9
Answer : B

Question : If the radius of the base of a right circular cylinder is halved, keeping the height same, the ratio of the volume of the reduced cylinder to that of original cylinder is
a) 2 : 3
b) 3 : 4
c) 1 : 4
d) 4 : 1
Answer : C

Question : The circumference of the edge of a hemispherical bowl is 132 cm. When 𝜋 is taken as 22/7 the capacity of the bowl in 𝑐𝑚3 is :
a) 2772
b) 924
c) 19404
d) 9702
Answer : C

Question : A shuttlecock used for playing badminton has the shape of the combination of
(a) a cylinder and a sphere
(b) a sphere and a cone
(c) a cylinder and a hemisphere
(d) frustum of a cone and a hemisphere
Answer : D

Question : The shape of an ice-cream cone is a combination of:
(a) Sphere + cylinder
(b) Sphere + cone
(c) Hemisphere + cylinder
(d) Hemisphere + cone
Answer : D

Question : The total surface area of a hemispherical solid having radius 7 cm is
(a) 462 cm²
(b) 294 cm²
(c) 588 cm²
(d) 154 cm²
Answer : A

Question : The radii of the top and bottom of a bucket of slant height 13 cm are 9 cm and 4 cm respectively. The height of the bucket is
(a) 10 cm
(b) 12 cm
(c) 15 cm
(d) 16 cm
Answer : B

Question : A cylinder and a cone are of same base radius and of same height. The ratio of the volume of the cylinder to that of the cone is
(a) 2 : 1
(b) 3 : 1
(c) 2 : 3
(d) 3 : 2
Answer : B

Question : The slant height of the frustum of a cone having radii of two ends as 5 cm and 2 cm respectively and height 4 cm is
(a) √26 cm
(b) 5 cm
(c) √65 cm
(d) 25 cm
Answer : B

Question : If two solid hemispheres of same base radius are joined together along their bases, then curved surface area of this new solid is
(a) 3πr²
(b) 4πr²
(c) 5πr²
(d) 6π
Answer : B

Question : A piece of paper is in the shape of a semi¬circular region of radius 10 cm. It is rolled to form a right circular cone. The slant height is
(a) 5 cm
(b) 10 cm
(c) 15 cm
(d) 20 cm
Answer : B

Question : The surface area of a sphere is 616 cm². Its radius is
(a) 7 cm
(b) 14 cm
(c) 21 cm
(d) 28 cm
Answer : A

Question : The base radii of two circular cones of the same height are in the ratio 3 : 5. The ratio of their volumes are
(a) 9 : 25
(b) 5 : 3
(c) 9 : 5
(d) 3 : 25
Answer : A

Question : The volume of a sphere is 4851 cm³. Its diameter is
(a) 3.5 cm
(b) 7 cm
(c) 14 cm
(d) 21 cm
Answer : D

Question : A solid formed on revolving a right angled triangle about its height is
(a) cylinder
(b) sphere
(c) right circular cone
(d) two cones
Answer : C

Question : If a cone is cut parallel to the base of it by a plane in two parts, then the shape of the top of the cone will be a:
(a) Sphere
(b) Cube
(c) Cone itself
(d) Cylinder
Answer : C

Question : The radius of a circle is 7 cm. What is the perimeter of the semi circle?
a) 36 cm
b) 14 cm
c) 7p
d) 14p
Answer : A

Question : The radius of two circles are 13 cm and 6 cm respectively. What is the radius of the circle which has circumference equal to the sum of the circumference of two circles?
a) 19 p
b) 19 cm
c) 25 cm
d) 32 cm
Answer : B

Question : The circumference of two circles are in the ratio 4 : 5 what is the ratio of the areas of these circles.?
a) 4:5
b) 16:25
c) 64:125
d) 8:10
Answer : B

Question : The volume of a cuboid is 440 cm³. The area of its base is 66 cm². What is its height?
a) 40/3 cm
b) 20/3 cm
c) 440 cm
d) 66 cm
Answer : B

Question : Volume of two cubes is in the ratio of 8 : 125. The ratio of their surface areas is
a) 8:125
b) 2:5
c) 4:25
d) 16:25
Answer : C

Question : If the perimeter of a sector is ‘l’ and radius is ‘r’ then the area of the sector is
a) l . r
b) l . r²
c) lr²/2
d) l². r
Answer : C

Question : Three cubes each of side ‘a’ are joined from end to end to form a cuboid. The volume of the new cuboids :
a) a²
b) 3a³
c) a³
d) 6a³
Answer : B

Question : A wire is in the form of a circle of radius 7 cm. It is bent into a square the area of the square is :
a) 11 cm²
b) 121 cm²
c) 154 cm²
d) 44 cm²
Answer : B

Question : If the radii of the circular ends of a conical bucket of height 45cm, are 28 cm and 7 cm, then the capacity of the bucket is :
(a) 48605 cm³. 
(b) 48510 cm³. 
(c) 48150 cm³. 
(d) 4715 cm³.
Answer : B

(a) 255 cm³. 

(b) 145 cm³. 

(c) 135 cm³. 

(d) 125 cm³.

Answer : A

 

Question : A conical flask has base of radius ‘a’ cm and height of ‘h’ cm. It is completely filled with milk. The milk is poured into a cylindrical thermos flask, whose base is of radius p cm. The height of the solution level in the flask is :

(a) h/3p²

(b) ha2 /3p²

(c) ha2 /3p

(d) ha /3p²

Answer : B

 

Question : A conical cavity is drilled in a circular cylinder of height 15 cm and base of radius 8 cm. The height and the base radius of the cone are also the same. Then, the whole surface of the remaining solid (in cm³) is :

(a) 240π. 

(b) 440π. 

(c) 640π. 

(d) 960π. 

Answer : B

 

CASE STUDY 1. One day Rinku was going home from school, saw a carpenter working on wood. He found that he is carving out a cone of same height and same diameter from a cylinder. The height of the cylinder is 24 ern and base radius is 7 cm. While watching this, some questions came into Rinkus mind. Help Rinku to find the answer of the following questions.

(i) After carving out cone from the cylinder,
(a) Volume of the cylindrical wood will decrease.
(b) Height of the cylindrical wood will increase.
(c) Volume of cylindrical wood will increase.
(d) Radius of the cylindrical wood will decrease.
Answer : A

(ii) Find the slant height of the conical cavity so formed.
Answer : - 25cm

(iii) The curved surface area of the conical cavity so formed is -----------------------
Answer : 175 𝜋 cm²

(iv) External curved surface area of the cylinder is_____.
Answer : 336 𝜋 cm²

(v) Volume of conical cavity is ------------------------
Answer : 392cm³

Case study question- 2
During Covid times people prefer using homogenized milk, UHT Processed and aseptically packed in an exceptional six layer, tamper-proof Tetra Packaging with 0% bacteria and 100% pure health. This new six layer interfere proof, prevents air and freshness, light and bacteria from entering the pack. As an effect, the milk stays fresh and pure for a minimum of 180 days until opened, even without refrigeration.The 500ml milk is packed in cuboidal containers of dimensions 15 x 8 x 5 . These milk packets are then packed in cuboidal cartons of dimension 30x 32 x 15.(All dimensions are in cm)

Based on the above given information answer the following questions

Question : Find the total surface area of a milk box.
a) 1890 cm²
b) 400 cm²
c) 470 cm²
d) 600 cm²
Answer : B

Question : How many milk packets can be filled in a carton?
a) 12
b) 24
c) 20
d) 8
Answer : C

Question : How much milk will the cup contain?
a) 1200 L
b) 1 L 100ml
c) 11 L 10 ml
d) 100 L
Answer : C

Question : How much cardboard is needed to make the carton if 10% of wastage is taken into account.
a) 3310 cm²
b) 2100 cm²
c) 4200 cm²
d) 3969 cm²
Answer : A

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 : A solid right cylinder cone is cut into two parts at the middle of its height by a plane parallel to its base. The ratio of the volume of the smaller cone to the whole cone is
(a) 1 : 2
(b) 1 : 4
(c) 1 : 6
(d) 1 : 8

Question : The total surface area of a hemisphere of radius ‘r’ is
(a) 2πr²
(b) 4πr²
(c) 3πr²
(d) 5πr²

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 : 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) 12∏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 ametal 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 : The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions to move once over to level a playground. The area of the playground in m² is:
(a) 1584
(b) 1284
(c) 1384
(d) 1184

Question : A cylindrical pillar is 50 cm in diameter and 3.5 m in height. The cost of painting its curved surface at the rate of Rs. 12.50 per m² is:
(a) Rs. 68.75
(b) Rs. 58.75
(c) Rs. 48.75
(d) Rs. 38.75

Question : The inner diameter of circular well is 3.5m. It is 10m deep. Its inner curved surface area in m² is:
(a) 120
(b) 110
(c) 130
(d) 140

Question : In a hot water heating system there is a cylindrical pipe of length 28 m and diameter 5 cm. The total radiating surface area in the system in m² is:
(a) 6.6
(b) 5.5
(c) 4.4
(d) 3.4

Question : The curved surface area of a right circular cone of slant height 10 cm and base radius 7 cm is
(a) 120 cm²
(b) 220 cm²
(c) 240 cm²
(d) 140 cm²

Question : The height of a cone is 16 cm and base radius is 12 cm. Its slant height is
(a) 10 cm
(b) 15 cm
(c) 20 cm
(d) 8 cm

Question : The curved surface area of a right circular cone of height 16 cm and base radius 12 cm is
(a) 753.6 cm²
(b) 1205.76 cm²
(c) 863.8 cm²
(d) 907.6 cm²

Question : The curved surface area of a right circular cone of slant height 10 cm and base radius 10.5 cm is
(a) 185 cm²
(b) 160 cm²
(c) 165 cm²
(d) 195 cm²

Question : The slant height of a cone is 26 cm and base diameter is 20 cm. Its height is
(a) 24 cm
(b) 25 cm
(c) 23 cm
(d) 35 cm

Question : The curved surface area of a cone is 308 cm² and its slant height is 14 cm. The radius of its base is
(a) 8 cm
(b) 7 cm
(c) 9 cm
(d) 12 cm

Question : A conical tent is 10 m high and the radius of its base is 24 m. The slant height of tent is
(a) 26 m
(b) 28 m
(c) 25 m
(d) 27 m

Question : The slant height and base diameter of a conical tomb are 25 m and 14 m respectively. The cost of white washing its curved surface at the rate of Rs. 210 per 100 m² is
(a) Rs. 1233
(b) Rs. 1155
(c) Rs. 1388
(d) Rs. 1432

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 48∏ 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 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 total surface area of a solid hemisphere of radius r is
(a) πr² 
(b) 2πr² 
(c) 3πr² 
(d) 4πr²

Question : The volume and the surface area of a sphere are numerically equal, then the radius of sphere is
(a) 0 units
(b) 1 units
(c) 2 units
(d) 3 units

Question : A cylinder, a cone and a hemisphere are of the same base and of the same height. The ratio of their volumes is
(a) 1 : 2 : 3
(b) 2 : 1 : 3
(c) 3 : 1 : 2
(d) 3 : 2 : 1

Question : Small spheres, each of radius 2cm, are made by melting a solid iron ball of radius 6cm, then the total number of small spheres is
(a) 9
(b) 6
(c) 27
(d) 81

Question : A solid sphere of radius r cm is melted and recast into the shape of a solid cone of height r. Then the radius of the base of cone is
(a) 2r
(b) r
(c) 4r
(d) 3r

Question : Three solid spheres of diameters 6cm, 8cm and 10cm are melted to form a single solid sphere. The diameter of the new sphere is
(a) 6 cm
(b) 4.5 cm
(c) 3 cm
(d) 12 cm

Question : The radii of the ends of a frustum of a cone 40 cm high are 38 cm and 8 cm. The slant height of the frustum of cone is
(a) 50 cm
(b) 10√7 cm
(c) 60.96 cm
(d) 4√2 cm

Question : The circular ends of a bucket are of radii 35 cm and 14 cm and the height of the bucket is 40 cm. Its volume is
(a) 60060 cm³ 
(b) 80080 cm³ 
(c) 70040 cm³ 
(d) 80160 cm³

Question : If the radii of the ends of a bucket are 5 cm and 15 cm and it is 24 cm high, then its surface area is
(a) 1815.3 cm² 
(b) 1711.3 cm² 
(c) 2025.3 cm² 
(d) 2360 cm²

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 : 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 /3 πr ² h
(c) πr ² h
(d) 2πr ² h

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

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 40p cm ² . 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