CBSE Class 9 Mathematics Surface areas and Volumes Assignment Set A

Question. If volume and surface area of a sphere are numerically equal, find its radius.
(A) 2 units
(B) 3 units
(C) 4 units
(D) 5 units
Answer : B

Question. The base radius of a cylinder is 1(2/3) times its height. The cost of painting it s C.S.A. at 2 paise/cm² is ₹ 92.40.What volume of the paint is req uired?
(A) 80850 cm³
(B) 80580 cm³
(C) 80508 cm³
(D) 85800 cm³
Answer : A

Question. A vessel is conical in shape. If its volume is 33.264 litres and height is 72 cm, what is the cost of repairing its C.S.A. at ₹ 12/sq. m?
(A) ₹ 5.94
(B) ₹ 6.94
(C) ₹ 7.95
(D) ₹ 7.59
Answer : A

Question. A joker's cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the areas of the sheet required to make 10 such caps.
(A) 5000 cm²
(B ) 6200 cm²
(C) 5500 cm²
(D) 6000 cm²
Answer :C

Question. A hemispherical bowl is made of steel of 0.25 em t hickness. The inner radius of the bowl is 5 cm. Find the volume of steel used.
(A) 42.15 cm³
(B) 41.52 cm³
(C) 41.28 cm³
(D) 45.21 cm³
Answer : C

Question. What is the length of the longest pole that can be put in a room of dimensions 10m x 10m x 5m?
(A) 15 m
(B) 16 m
(C) 1 0 m
(D) 12 m
Answer : A

Question. The cost of painting the T.S.A. of cone at 5 ps/cm² is ₹35.20. Determine the volume of the cone if its slant height is 25 cm.
(A) 1223 cm²
(B) 1232 cm²
(C) 1323 cm²
(D) 1332 cm²
Answer : B

Question. How many lit res of water flows out through a pipe having an area of crosssection of 5 cm2 in one minute, if the speed of water in pipe is 30 em/sec?
(A) 9 litres
(B) 15 litres
(C) 30 litres
(D) 3 litres
Answer : A

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

Question. Into a conical tent of radius 7 m and vertical height 4.5 m, how many full bags of rice can be empt ied, if volume of each bag is 1.5 m³.
(A) 120 bags
(B) 144 bags
(C) 154 bags
(D) 172 bags
Answer : B

Question.  A semi-ci rcular sheet of met al of diameter 28 em is bent into an open conical cup.
Find the capacity of the cup.
(A) 622 cm3
(B) 504 cm3
(C) 645 m³
(D) 592 m³
Answer : D

Question. The diameter of a garden roller is 1 .4 m and it is 2 m long. How much area will it cover in 5 revolutions? (Take π = 22/7)
(A) 11 sq. m
(B) 16 sq. m
(C) 28 sq. m
(D) 44 sq.m
Answer : D

Question. A right circular cylinder has a height of 21 em and base radius of 5 cm. Find the curved surface area of the cylinder
(A) 230 cm² 
(B) 660 cm²
(C) 550 cm²
(D) 450 cm²
Answer : B

Question. The area of the curved surface of a right circular cylinder is 4400 cm² and the circumference of its base is 110 cm. Find the height of the cylinder
(A) 30 cm
(B) 10 cm
(C) 20 cm
(D) 40 cm
Answer : D

Question. Find the largest volume (in cm3) of a cube that can be enclosed in a sphere of diamet er 2 cm.
(A) 1
(B) 2√2
(C) π
(D) 8/3√3
Answer : B

Question. Find the curved surface of a right circular cone, whose slant height and the base radius are 25 cm and 7 cm respectively.
(A) 420 cm²
(B) 550 cm²
(C) 460 cm²
(D) 580 cm²
Answer : B

Question. A cylindrical vessel of diameter 9 cm has some water in it. A cylindrical iron piece of diameter 6 cm and height 4.5 em is dropped in it. After it was completely immersed, find the rise in t he level of water.
(A) 0.8 cm
(B) 2 cm
(C) 1 cm
(D) 0.4 cm
Answer : B

Question. A well, 14 m deep is 2 m in radius. Find the cost of cement ing the inner curved surface at the rate of ₹ 2 per square metre.
(A) ₹ 242
(B) ₹ 352
(C) ₹ 464
(D) ₹ 294
Answer : B

Question. The radius of a sphere is increased by P%.
What is the increase in its surface area?
(A) P %
(B) P² %
(C) (2P + P²/100) %
(D) P²/2 %
Answer : C

Question. If l is the length of a diagonal of a cube of volume V, what is t he relat ion between l and V?
(A) 3V = l³
(B) √3V = l³
(C) 3-./3 V = 2l³
(D) 3-/3V= l³
Answer : D

Question. If each edge of a cube is increased by 50%, what is the percentage increase in its surface area?
(A) 50%
(B) 75%
(C) 100%
(D) 125%
Answer : D

Question. A spherical ball of diameter 21 cm, is melted and recasted into cubes, each of side 1 cm. Find the number of cubes thus formed. (Use π = 22/7)
(A) 2057
(B) 1962
(C) 4851
(D) 3272
Answer : C

Question. If the areas of the adjacent faces of a rectangular block are in the ratio 2 : 3 : 4 and its volume is 9000 cm³, what is the length of the shortest edge?
(A) 30 cm
(B) 20 cm
(C) 15 cm
(D) 10 cm
Answer : C

Question. If 10 cubic metres of clay is uniformly spread on a land of area 10 ares, what is the rise in the level of the ground?
(A) 1 cm
(B) 10 cm
(C) 100 cm
(D) 1000 cm
Answer : A

Question. Volume of a cuboid is 12 cm³. Find t he volume (in cm³) of the cuboid if its sides are double.
(A) 24
(B) 48
(C) 72
(D) 96
Answer : D

Question. The largest sphere is carved out of a cube of side 7 cm. Find t he volume of the sphere. (Take n = 3.14.)
(A) 152.74 cm³
(B) 243.41 cm³
(C) 179.67 cm³
(D) 195.01 cm³
Answer : C

Question. If each edge of a cube, of volume, V, is doubled, find the volume of the new cube.
(A) 2V
(B) 4V
(C) 6V
(D) 8V
Answer : D

Question. Two cubes of side 6 em each are joined end to end. Find the surface area of the resultant cuboid.
(A) 200 cm²
(B) 420 cm²
(C) 360 cm²
(D) 270 cm²
Answer : C

Question. What is the ratio of volumes of two cones with the same radii?
(A) h, : h²
(B) r, : r²
(C) s, : s²
(D) 1 : 2
Answer : A

Question. The curved surface area of a right circular cylinder of height 14 em is 88 cm². Find the volume of the cylinder. (Take π = 22/7)
(A) 22 cm³
(B) 44 cm³
(C) 88 cm³
(D) 11 cm³
Answer : B

Question. If A₁ A₂ and A₃ denote the areas of three adjacent faces of a cuboid, find it s volume
(A) A₁ A₂ A₃
(B) 2A₁ A₂ A₃
(C) √A₁ A₂ A₃
(D) √A₁ A₂ A₃
Answer : C

Question. If 5 men are in a room of dimensions 3 m x 4 m x 10 m, what is the amount of air available for each of them?
(A) 48m³
(B) 36m³
(C) 24m³
(D) 120m³
Answer : C

Question. If each edge of a cube of surface area S is doubled, what is the surface area of the new cube?
(A) 2$
(B) 4$
(C) 6$
(D) 8$
Answer : B

Question. Find t he cost of constructing a wall 8 m long,4 m high and 20 em thick at the rate of ₹ 25 per m³.
(A) ₹ 16
(B) ₹ 80
(C) ₹ 160
(D) ₹ 320
Answer : C

Question. If the diameter of the base of a closed right circular hcylinder is equal to its height h, find its total surface area.
(A) 2nh²
(B) (3/2) nh²
(C) (4/3) nh²
(D) nh²
Answer : B

Question. The radius of a wire is decreased to its one-t hird. If its volume remains the same, by how many t imes will its length increase?
(A) 3 t imes
(B) 6 times
(C) 9 times
(D) 27 times
Answer : C

Case Based MCQs

Case I : Read the following passage and answer the questions from 1 to 2.
A class teacher brings some clay in the classroom to teach the topic mensuration. First she forms a cylinder of radius 6 cm and height 8 cm and then she moulds that cylinder into sphere.

1. Find the volume of the cylindrical shape.
(a) 288 π cm³
(b) 244 π cm3
(c) 240 π cm³
(d) 216 π cm³
Answer : A

2. The formula for ‘volume of sphere’ is
(a) (4/3)πr²
(b) πr²h
(c) (4/3)³ πr
(d) (2/3)πr³
Answer : C

3. When clay changes into one shape to other, which of the following remains same?
(a) Area
(b) C.S.A
(c) Radius
(d) Volume
Answer : D

4. The radius of the sphere is
(a) 2 cm
(b) 4 cm
(c) 5 cm
(d) 6 cm
Answer : D

5. Find the volume of sphere, the teacher made.
(a) 288π cm³
(b) 184π cm³
(c) 240π cm³
(d) 216π cm³
Answer : A

Case II : Read the following passage and answer the questions from 1 to 5.
Ankita realised the need of food for birds on her terrace and decided to make a bird feeder. She got a flexible plastic rectangular sheet of size 44 cm × 15 cm. She rolled it along its length and joined the two opposite ends using a tape for circular base of cylinder. She found a square sheet of size 15 cm × 15 cm by cutting it into required circular shape she prepared the bird feeder as shown in figure.

1. The curved surface area of the cylinder formed is
(a) 550 cm²
(b) 660 cm²
(c) 430 cm²
(d) 840 cm²
Answer : B

2. The radius of the base of the cylinder is
(a) 5 cm
(b) 6 cm
(c) 7 cm
(d) 8 cm
Answer : C

3. The area of the circular base required for the cylinder is
(a) 154 cm²
(b) 164 cm²
(c) 240 cm²
(d) 184 cm²
Answer : A

4. How much will be the area of square sheet left unused after removing the circular base of the cylinder from it?
(a) 78 cm²
(b) 62 cm²
(c) 75 cm²
(d) 71 cm²
Answer : D

5. Volume of the seeds that can be filled in the cylinder, for birds is
(a) 2310 cm³
(b) 2425 cm³
(c) 2623 cm³
(d) 2810 cm³
Answer : A

 

Assertion & Reasoning Based MCQs

Directions (Q.1 to 5) : In these questions, a statement of Assertion is followed by a statement of Reason is given.
Choose the correct answer out of the following choices :
(a) Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
(b) Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
(c) Assertion is correct statement but Reason is wrong statement.
(d) Assertion is wrong statement but Reason is correct statement.

1. Assertion : The external dimensions of a wooden box are 18 cm, 10 cm and 6 cm respectively and thickness of the wood is 5 mm, then the internal volume is 765 cm³.
Reason : If external dimensions of a rectangular box be l, b and h and the thickness of its sides be x, then its internal volume is (l – 2x)(b – 2x)(h – 2x).
Answer : A

2. Assertion : A cone is a solid figure.
Reason : A cone is generated when rectangular sheet is rotated about its axis.
Answer : C

3. Assertion : If curved surface area of a cone is 550 cm² and its diameter is 14 cm. Then, its slant height will be 20 cm.
Reason : Curved surface area of a cone having base radius r and slant height l is πrl.
Answer : D

4. Assertion : If the radius of a sphere is tripled, then the ratio of the volume of the original sphere to that of the new is 1 : 27.
Reason : Volume of a sphere with radius r is 4πr³.
Answer : C

5. Assertion : If a cone and a hemisphere have equal base and volume, then the ratio of their heights is 2 : 1.
Reason : Volume of a cylinder of height h and base radius r is πr²h.
Answer : B

Very Short Answer Type Questions

Question. A metal sheet 27 cm long, 8 cm broad and 1 cm thick is melted and recast into a cube. Then find the volume of cube formed.
Answer : Volume of sheet = (27 × 8 × 1) cm³
= 216 cm³
Volume of cube formed = 216 cm³

Question. The dimensions of an open box are 52 cm, 40 cm and 29 cm. Its thickness is 2 cm. If 1 cm³ of metal used in the box weighs 0.5 gms, then find the weight of the box.
Answer : Volume of metal
= (52 × 40 × 29 – 48 × 36 × 27) cm³ = 13664 cm³
∴ Weight of the box = (13664 x 0 5/1000). kg = 6.832 kg

Question. The radius of a circular cylinder is same as that of a sphere. Their volumes are equal.
Then find height of the cylinder.
Answer : Let h be the height of cylinder.
Radius of cylinder = Radius of sphere = r
Then, we have (4/3)πr³ = πr²h ⇒ h = (4/3)r
∴ Height of cylinder = 4/3 times its radius

Question. The dimensions of a cinema hall are 120 m, 50 m, 30 m. Then find the volume of hall.
Answer : Length(l) = 120 m, Breadth(b) = 50 m, Height (h) = 30 m
Since the shape of cinema hall is of cuboid
∴ Volume of hall = l × b × h
= 120 × 50 × 30 m3 = 180000 m³

Question. A teak wood log is in the form of a cuboid of volume 76800 m³. How many rectangular planks of size 40 m × 12 m × 20 m can be cut from the cuboid?
Answer : 8. Number of rectangular planks
= Volume of cuboid of wood log/Volume of one plank = 76800/40x12x20 = 8

Question. Area of base of a solid hemisphere is 81π sq. cm. Then find its volume.
Answer : Let r be the radius of the hemisphere.
∴ πr² = 81π ⇒ r² = 81 ⇒ r = 9 cm.
Volume of hemisphere = (2/3)πr³ = (2/3)π(9)³ 486π cm³
 

SECTION A: (1 MARK)

1. A cylindrical piece of maximum volume has to be cut of an iron cube of edge 4 cm. Find the volume of the cylinder? (50.29cm³)

2. If each bag containing rice occupies 2.1 m³ of space, then find the number of full bags which can be emptied into a drum of radius 4.2 m and height 3.5 m (92)

3. If a square paper of side 25 cm is rolled to form a cylinder, then find its curved surface area? (625 cm²)

SECTION B: (2 MARKS)

4. If a hollow sphere of internal and external diameters 4 cm and 8 cm respectively melted into a cone of base diameter 8 cm, find the height of the cone? (14 cm)

5. Three cubes of metal whose edges are in the ratio 3:4:5 are melted down into a single cube whose diagonal is 12 √3 cm. Find the edges of the three cubes (6 cm 8 cm 10 cm)

6. Find the length of wire of diameter 2/5 cm that can be drawn from a solid sphere of radius 9 cm  (243 m)

7. A solid sphere of radius 6 cm is melted into a hollow cylinder of uniform thickness. If the external radius of the base of the cylinder is 5 cm and its height is 32 cm, find the uniform thickness of the cylinder  (1cm)

SECTION C: (3 MARKS)

8. Water flows out through a circular pipe whose internal diameter is 2 cm at the rate of 0.8 m/s into a cylindrical tank, the radius of whose base is 40 cm. By how much will the level rise in one and a half hour? ( 2.7 m)

9. A semicircular sheet of metal of radius 14 cm is bent into an open conical cup.

Find the depth, curved surface area and capacity of the cup? √3 = 1.73(12.11 cm 266.42 cm2 621.647cm³)

10. The surface area of a sphere of radius 5 cm is five times the area of the curved surface of a cone of radius 4 cm. Find the height and volume of the cone? (3 cm 352/7 cm³)

11. The radius of a sphere is increased by 10%. Find the percentage increase in volume  (33.1 %)

 

Please click the link below to download CBSE Class 9 Mathematics Surface areas and Volumes Assignment Set A