Please refer to the MCQ Questions for Class 9 Mathematics Chapter 13 Surface Areas and Volumes with Answers. The following Surface Areas and Volumes Class 9 Mathematics MCQ Questions have been designed based on the latest syllabus and examination pattern for Class 9. Our experts have designed MCQ Questions for Class 9 Mathematics with Answers for all chapters in your NCERT Class 9 Mathematics book.

## Surface Areas and Volumes Class 9 MCQ Questions with Answers

See below Surface Areas and Volumes Class 9 Mathematics MCQ Questions, solve the questions and compare your answers with the solutions provided below.

**Question. A cylindrical vessel of radius 16 cm contains water to a depth of 30 cm. If a spherical ball of brass is dropped into it and the water rises by 9 cm, then the radius of the ball is**

(a) 12 cm

(b) 15 cm

(c) 8 cm

(d) 18 cm

## Answer

A

**Question. The difference between the total surface area of a cube of side 4 cm and its lateral surface area is**

(a) 16 cm^{2}

(b) 20 cm^{2}

(c) 32 cm^{2}

(d) 24 cm^{2}

## Answer

C

**Question. The volume of resulting cuboid formed when two cubes each of side 6 cm are joined end to end is**

(a) 648 cm^{3}

(b) 864 cm^{3}

(c) 432 cm^{3}

(d) 416 cm^{3}

## Answer

C

**Question. The number of planks of dimensions (5 m × 25 cm × 10 cm) that can be placed in a pit which is 20 m long, 6 m wide and 80 cm deep is**

(a) 764

(b) 840

(c) 768

(d) 960

## Answer

C

**Question. Τhe number of 6 m cubes that can be formed from another cuboid measuring 18 m × 12 m × 9 m is****(a) 9**

(b) 10

(c) 12

(d) 15

## Answer

D

**Question. The length of the longest rod that can be placed in a room 12 m long, 9 m broad and 8 m high is**

(a) 15 m

(b) 20 m

(c) 18 m

(d) 17 m

## Answer

D

**Question. The edge of a cube whose volume is equal to the volume of a cuboid of dimensions 36 cm × 75 cm × 80 cm is**

(a) 48 cm

(b) 60 cm

(c) 36 cm

(d) 42 cm

## Answer

B

**Question. A rectangular pit of dimensions 30 m × 15 m × 12 m is dug and the earth taken out is disposed of in a carrier which can carry a maximum load of 540 m ^{3} of earth. The least number of rounds the carrier had to make to dispose of the earth dug out is**

(a) 20

(b) 10

(c) 15

(d) 12

## Answer

B

**Question. A granary is in the shape of a cuboid of size 16 m × 12 m × 9 m. If a bag of grain occupies a space of 0.48 m ^{3}, then the maximum number of bags that can be stored in the granary is**

(a) 1800

(b) 3600

(c) 2400

(d) 3000

## Answer

B

**Question. The volume of a right circular cylinder is 2310 cm ^{3}. If the radius of its base is 7 cm, then its height is**

(a) 7.5 cm

(b) 22.5 cm

(c) 15 cm

(d) 30 cm

## Answer

C

**Question. If a square paper of side 25 cm is rolled to form a cylinder, then its curved surface area is**

(a) 625 cm^{2}

(b) 500 cm^{2}

(c) 250 cm^{2}

(d) 1000 cm^{2}

## Answer

A

**Question. The volume of a cube whose diagonal is 2√3 cm is**

(a) 8 cm^{3}

(b) 4 cm^{3}

(c) 83 cm^{3}

(d) 4√3 cm^{3}

## Answer

A

**Question. The curved surface area of a cylinder whose circumference of the base is 22 m and height 3 m is**

(a) 66 m^{2}

(b) 132 m^{2}

(c) 33 m^{2}

(d) 99 m^{2}

## Answer

A

**Question. A conical tent is 21 m high and the diameter of its base is 4 m. If 10 men sleep in it, then the average number of cubic dm of air space per man is**(a) 4400

(b) 8800

(c) 8400

(d) 4800

## Answer

B

**Question. If the outer diameter of a pipe 21 m long is 1 m, then its outer curved surface area is**

(a) 21 m^{2}

(b) 63 m^{2}

(c) 66 m^{2}

(d) 42 m^{2}

## Answer

C

**Question. The cost of cementing the inner curved surface of a 14 m deep well of radius 2 m at the rate of Rs 2 per m2 is**

(a) Rs 352

(b) Rs 56

(c) Rs 112

(d) Rs 176

## Answer

A

**Question. If a conical glass is 35 cm in diameter and 12 cm deep, then its capacity in litres is**

(a) 1.155 L

(b) 3.85 L

(c) 0.5775 L

(d) 7.7 L

## Answer

B

**Question. If the lateral surface area of a cylinder is 132 cm ^{2} and its height is 7 cm, then its base diameter is**

(a) 5 cm

(b) 3 cm

(c) 6 cm

(d) 4 cm

## Answer

C

**Question. The area of canvas required for a conical tent of height 24 m and base radius 7 m is**

(a) 550 m^{2}

(b) 1100 m^{2}

(c) 275 m^{2}

(d) 825 m^{2}

## Answer

A

**Question. The circumference of the base of a right circular cylinder is 44 cm. If its whole surface area is 968 cm ^{2}, then the sum of its height and radius is**

(a) 16 cm

(b) 18 cm

(c) 20 cm

(d) 22 cm

## Answer

D

**Question. The diameter of the base of a cylinder of curved surface area 88 cm ^{2}and height 14 cm is**

(a) 1 cm

(b) 2 cm

(c) 1.5 cm

(d) 2.5 cm

## Answer

B

**Question. A cylindrical piece of maximum volume has to be cut out of an iron cube of edge 4 cm. Then, the maximum volume of the iron cylinder is**

(a) 32π cm^{3}

(b) 24π cm^{3}

(c) 16π cm^{3}

(d) 28π cm^{3}

## Answer

C

**Question. The cost of digging a pit of dimensions 4.5 m × 2.5 m × 2.5 m at the rate of` 20 per cubic metre is**

(a) Rs 281.25

(b) Rs 562.50

(c) Rs 1125

(d) Rs 1687.50

## Answer

B

**Question. If each bag containing rice occupies 2.1 m ^{3} of space, then the number of full bags which can be emptied into a drum of radius 4.2 m and height 3.5 m is**

(a) 69

(b) 46

(c) 92

(d) 138

## Answer

C

**Question. If the radius of the base of a right circular cylinder is halved, keeping the same height, then the ratio of the volume of the reduced cylinder to the volume of the original cylinder is**

(a) 1 : 4

(b) 4 : 1

(c) 1 : 2

(d) 2 : 1

## Answer

A

**Question. The total surface area of a cube is 96 cm ^{2}. The volume of the cube is**

(a) 27 cm

^{3}

(b) 64 cm

^{3}

(c) 8 cm

^{3}

(d) 512 cm

^{3}

## Answer

B

**Question. The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio of 5 : 3. The ratio of their volumes is**

(a) 20 : 27

(b) 20 : 37

(c) 17 : 27

(d) 10 : 17

## Answer

A

**Question. The volume of a sphere of diameter 42 cm is**

(a) 38000 cm^{3}

(b) 34000 cm^{3}

(c) 30000 cm^{3}

(d) 38808 cm^{3}

## Answer

D

**Question. The volume of a sphere is numerically equal to its surface area, then its diameter is**

(a) 6 units

(b) 3 units

(c) 1 unit

(d) 2 units

## Answer

A

**Question. A cube of side 4 cm contains a sphere touching its sides. Find the approximate volume of the gap in between.**

(a) 33 cm^{3}

(b) 30.48 cm^{3}

(c) 33.52 cm^{3}

(d) 34 cm^{3}

## Answer

B

**Question. The ratio of the radii of two spheres whose volumes are in the ratio 64 : 27 is**

(a) 16 : 9

(b) 8 : 3

(c) 10 : 7

(d) 4 : 3

## Answer

D

**Question. Given that the surface area of a spherical shot-put is 616 cm2, its diameter is**

(a) 12 cm

(b) 14 cm

(c) 16 cm

(d) 18 cm

## Answer

B

**Question. If a sphere of radius 3 cm is melted and recast into a right circular cone of height 3 cm, then the radius of the base of the cone is**

(a) 27 cm

(b) 3 cm

(c) 6 cm

(d) 9 cm

## Answer

C

**Question. If a spherical balloon grows to twice its radius when inflated, then the ratio of the volume of the inflated balloon to the original balloon is**

(a) 8 : 1

(b) 4 : 1

(c) 6 : 1

(d) 5 : 1

## Answer

A

**Question. If the total surface area of a hemisphere is 1848 cm2, then its diameter is**

(a) 22 cm

(b) 26 cm

(c) 28 cm

(d) 24 cm

## Answer

C

**Question. The total surface area of a cone of radius 2r and slant height l/2 is**

(a) 2πr(l + r)

(b) πr(l+r/4)

(c) πr(4r + l)

(d) 2πr

## Answer

C

**Question. The total surface area of a cone of radius 7 m and slant height 10 m is**

(a) 374 m^{2}

(b) 598.4 m^{2}

(c) 561 m^{2}

(d) 280.5 m^{2}

## Answer

A

**Question. The diameter of the base of a cone of height 15 cm and volume 770 cm ^{3} is**

(a) 7 cm

(b) 14 cm

(c) 21 cm

(d) 10.5 cm

## Answer

B

**Question. The surface area of a sphere of radius 3.5 cm is**

(a) 77 cm^{2}

(b) 154 cm^{2}

(c) 154 cm^{2}

(d) 120 cm^{2}

## Answer

C

**Question. The volume of a cone is 1570 cm ^{3}. If it is 15 cm high then its base area is**

(a) 415 cm

^{2}

(b) 413 cm

^{2}

(c) 314 cm

^{2}

(d) 514 cm

^{2}

## Answer

C

**Question. If the area of the base of a right circular cylinder is 15400 cm ^{2} and its volume is 92400 cm^{3}, then its curved surface area is**

(a) 2880 cm

^{2}

(b) 2760 cm

^{2}

(c) 2640 cm

^{2}

(d) 2600 cm

^{2}

## Answer

C

**Question. A conical pandal 240 m in radius and 100 m high is made of cloth which is 100π m wide. Then, the length of cloth used to make the pandal is**

(a) 625 m

(b) 676 m

(c) 600 m

(d) 624 m

## Answer

D

**Question. The curved surface area of a cylinder and a cone is equal. If their base radius is same, then the ratio of the slant height of the cone to the height of the cylinder is**

(a) 2 : 3

(b) 1 : 1

(c) 2 : 1

(d) 1 : 2

## Answer

C

**Question. If the ratio of the radii of bases of two cones is 3 : 1 and the ratio of their heights is 1 : 3, then the ratio of their volumes is**

(a) 1 : 2

(b) 2 : 1

(c) 1 : 3

(d) 3 : 1

## Answer

D

**Question. If a sphere of radius 2r has the same volume as that of a cone with a circular base of radius r, then the height of the cone is**

(a) 32r

(b) 30r

(c) 28r

(d) 24r

## Answer

A

**Question. The surface area of a cuboid whose length, breadth and height are 15 cm, 10 cm and 20 cm respectively is**

(a) 1300 cm^{2}

(b) 650 cm^{2}

(c) 1950 cm^{2}

(d) 2600 cm^{2}

## Answer

A

**Question. The total surface area of a right circular cylinder of height 4 cm and radius 3 cm is**

(a) 132 cm^{2}

(b) 66 cm^{2}

(c) 198 cm^{2}

(d) 99 cm^{2}

## Answer

A

**Question. The difference between the total surface area and the lateral surface area of a cuboid of length 20 cm, breadth 10 cm and height 40 cm is**

(a) 400 cm^{2}

(b) 800 cm^{2}

(c) 200 cm^{2}

(d) 600 cm^{2}

## Answer

A

**Question. If the radius (r) of a sphere is reduced to its half, then new volume would be**

(a) 1/2(4/3πr^{3})

(b) 4/3.π(r^{3}/2)

(c) 4/3.π(r^{3}/8)

(d) 4/6.π(r^{3}/8)

## Answer

C

**Question. The volume of a cylinder whose circumference of the base is 132 cm and height 25 cm is**

(a) 3300 cm^{3}

(b) 34650 cm^{3}

(c) 9900 cm^{3}

(d) 19800 cm^{3}

## Answer

B

**Question. A cylinder and a cone have equal base radius. If their volumes are same, then the ratio of the height of the cylinder to the height of the cone is**

(a) 1 : 3

(b) 1 : 2

(c) 2 : 1

(d) 3 : 1

## Answer

A

**Question. The total surface area of a 7 cm high cylinder having a volume of 448π cm3 is**

(a) 5110/7 cm^{2}

(b) 5280/7 cm^{2}

(c) 5287/7 cm^{2}

(d) 755 cm^{2}

## Answer

B

**Question. The curved surface area of a well of diameter 3.5 m and depth 10 m is**

(a) 135 m^{2}

(b) 35 m^{2}

(c) 70 m^{2}

(d) 110 m^{2}

## Answer

D

**Question. If the circumference of the base of a 9 m high conical tent is 44 m, then the volume of air contained in it is**

(a) 693 m^{3}

(b) 924 m^{3}

(c) 1386 m^{3}

(d) 462 m^{3}

## Answer

D

**Question. To make a closed hollow cone of base radius 7 cm and height 24 cm, the area of metal sheet required is**

(a) 550 cm^{2}

(b) 704 cm^{2}

(c) 825 cm^{2}

(d) 1100 cm^{2}

## Answer

B

**Question. The curved surface area of a right circular cylinder is 4400 cm ^{2}. If the circumference of its base is 110 cm, then its height is**

(a) 36 cm

(b) 38 cm

(c) 40 cm

(d) 42 cm

## Answer

C

**Question. A conical vessel whose internal depth is 42 cm and internal diameter is 48 cm is full of water. If 1 cubic dm of water weighs 1 kg-wt, then the weight of water in the conical vessel is**

(a) 26.5 kg-wt

(b) 25.344 kg-wt

(c) 25.5 kg-wt

(d) 25.65 kg-wt

## Answer

B

**Question. If the slant height of a cone of base radius 7 cm is 25 cm, then its height is**

(a) 32 cm

(b) 24 cm

(c) 18 cm

(d) 36 cm

## Answer

B

**Question. The height of a conical vessel is 3.5 cm. If its capacity is 3.3 litres of milk, then the diameter of its base is**

(a) 30 cm

(b) 60 cm

(c) 15 cm

(d) 35 cm

## Answer

B

**Question. If the volume of a sphere is 4851 cm ^{3}, then its surface area is**

(a) 693 cm

^{2}

(b) 1386 cm

^{2}

(c) 2079 cm

^{2}

(d) 1039.5 cm

^{2}

## Answer

B

**Question. The number of litres that a cuboidal water tank of dimensions 6 m × 5 m × 4.5 m can hold is**

(a) 135000 L

(b) 135 L

(c) 270 L

(d) 270000 L

## Answer

A

**Question. A hemispherical bowl is made of steel 0.25 cm thick. If the inner radius of the bowl is 3.25 cm, then the outer curved surface area of the bowl is**

(a) 77 cm^{2}

(b) 154 cm^{2}

(c) 38.5 cm^{2}

(d) 115.5 cm^{2}

## Answer

A

**Question. If the surface area of a solid sphere is 1386 cm ^{2}, then the total surface area of the solid hemisphere of the same radius is**

(a) 693 cm

^{2}

(b) 1039.5 cm

^{2}

(c) 519.75 cm

^{2}

(d) 1559.25 cm

^{2}

## Answer

B

**Question. The number of spherical bullets each 5 dm in diameter which can be cast from a rectangular block of lead 11 m long, 10 m broad and 5 m high is**

(a) 8400

(b) 4200

(c) 6300

(d) 5600

## Answer

A

**Question. The number of solid spheres each 6 cm in diameter, which can be moulded from a solid cylinder of height 45 cm and diameter 4 cm without any loss is**

(a) 7

(b) 12

(c) 10

(d) 5

## Answer

D

**Question. If a hollow sphere of internal and external diameters 4 cm and 8 cm respectively melted into a cone of base diameter 8 cm, then the height of the cone formed is**

(a) 14 cm

(b) 12 cm

(c) 16 cm

(d) 8 cm

## Answer

A

**Question. When a cuboid of dimensions 30 cm × 30 cm × 42.6 cm is melted and converted into cubes of edge 3 cm, then the number of cubes formed is**

(a) 2840

(b) 2130

(c) 1420

(d) 710

## Answer

C

**Question. If the radius and slant height of a cone are in the ratio 7 : 13 and its curved surface area is 286 cm2, then its radius is**

(a) 7 cm

(b) 10 cm

(c) 10.5 cm

(d) 7.5 cm

## Answer

A

**Question. The curved surface area of a right circular cylinder which just encloses a sphere of radius r is**

(a) 2πr^{2}

(b) 4πr^{2}

(c) 8πr^{2}

(d) 6πrr^{2}

## Answer

B

**Question. The number of cubes whose edge measures 3 cm, that can be formed by melting a cubic block of metal of edge 15 cm is**

(a) 125

(b) 45

(c) 75

(d) 135

## Answer

A