# MCQs For NCERT Class 9 Mathematics Chapter 13 Surface Areas and Volumes

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

A

Question. The difference between the total surface area of a cube of side 4 cm and its lateral surface area is
(a) 16 cm2
(b) 20 cm2
(c) 32 cm2
(d) 24 cm2

C

Question. The volume of resulting cuboid formed when two cubes each of side 6 cm are joined end to end is
(a) 648 cm3
(b) 864 cm3
(c) 432 cm3
(d) 416 cm3

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

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

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

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

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 m3 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

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 m3, then the maximum number of bags that can be stored in the granary is
(a) 1800
(b) 3600
(c) 2400
(d) 3000

B

Question. The volume of a right circular cylinder is 2310 cm3. 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

C

Question. If a square paper of side 25 cm is rolled to form a cylinder, then its curved surface area is
(a) 625 cm2
(b) 500 cm2
(c) 250 cm2
(d) 1000 cm2

A

Question. The volume of a cube whose diagonal is 2√3 cm is
(a) 8 cm3
(b) 4 cm3
(c) 83 cm3
(d) 4√3 cm3

A

Question. The curved surface area of a cylinder whose circumference of the base is 22 m and height 3 m is
(a) 66 m2
(b) 132 m2
(c) 33 m2
(d) 99 m2

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

B

Question. If the outer diameter of a pipe 21 m long is 1 m, then its outer curved surface area is
(a) 21 m2
(b) 63 m2
(c) 66 m2
(d) 42 m2

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

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

B

Question. If the lateral surface area of a cylinder is 132 cm2 and its height is 7 cm, then its base diameter is
(a) 5 cm
(b) 3 cm
(c) 6 cm
(d) 4 cm

C

Question. The area of canvas required for a conical tent of height 24 m and base radius 7 m is
(a) 550 m2
(b) 1100 m2
(c) 275 m2
(d) 825 m2

A

Question. The circumference of the base of a right circular cylinder is 44 cm. If its whole surface area is 968 cm2, then the sum of its height and radius is
(a) 16 cm
(b) 18 cm
(c) 20 cm
(d) 22 cm

D

Question. The diameter of the base of a cylinder of curved surface area 88 cm2and height 14 cm is
(a) 1 cm
(b) 2 cm
(c) 1.5 cm
(d) 2.5 cm

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 cm3
(b) 24π cm3
(c) 16π cm3
(d) 28π cm3

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

B

Question. If each bag containing rice occupies 2.1 m3 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

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

A

Question. The total surface area of a cube is 96 cm2. The volume of the cube is
(a) 27 cm3
(b) 64 cm3
(c) 8 cm3
(d) 512 cm3

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

A

Question. The volume of a sphere of diameter 42 cm is
(a) 38000 cm3
(b) 34000 cm3
(c) 30000 cm3
(d) 38808 cm3

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

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 cm3
(b) 30.48 cm3
(c) 33.52 cm3
(d) 34 cm3

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

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

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

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

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

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

C

Question. The total surface area of a cone of radius 7 m and slant height 10 m is
(a) 374 m2
(b) 598.4 m2
(c) 561 m2
(d) 280.5 m2

A

Question. The diameter of the base of a cone of height 15 cm and volume 770 cm3 is
(a) 7 cm
(b) 14 cm
(c) 21 cm
(d) 10.5 cm

B

Question. The surface area of a sphere of radius 3.5 cm is
(a) 77 cm2
(b) 154 cm2
(c) 154 cm2
(d) 120 cm2

C

Question. The volume of a cone is 1570 cm3. If it is 15 cm high then its base area is
(a) 415 cm2
(b) 413 cm2
(c) 314 cm2
(d) 514 cm2

C

Question. If the area of the base of a right circular cylinder is 15400 cm2 and its volume is 92400 cm3, then its curved surface area is
(a) 2880 cm2
(b) 2760 cm2
(c) 2640 cm2
(d) 2600 cm2

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

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

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

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

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 cm2
(b) 650 cm2
(c) 1950 cm2
(d) 2600 cm2

A

Question. The total surface area of a right circular cylinder of height 4 cm and radius 3 cm is
(a) 132 cm2
(b) 66 cm2
(c) 198 cm2
(d) 99 cm2

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 cm2
(b) 800 cm2
(c) 200 cm2
(d) 600 cm2

A

Question. If the radius (r) of a sphere is reduced to its half, then new volume would be
(a) 1/2(4/3πr3)
(b) 4/3.π(r3/2)
(c) 4/3.π(r3/8)
(d) 4/6.π(r3/8)

C

Question. The volume of a cylinder whose circumference of the base is 132 cm and height 25 cm is
(a) 3300 cm3
(b) 34650 cm3
(c) 9900 cm3
(d) 19800 cm3

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

A

Question. The total surface area of a 7 cm high cylinder having a volume of 448π cm3 is
(a) 5110/7 cm2
(b) 5280/7 cm2
(c) 5287/7 cm2
(d) 755 cm2

B

Question. The curved surface area of a well of diameter 3.5 m and depth 10 m is
(a) 135 m2
(b) 35 m2
(c) 70 m2
(d) 110 m2

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 m3
(b) 924 m3
(c) 1386 m3
(d) 462 m3

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 cm2
(b) 704 cm2
(c) 825 cm2
(d) 1100 cm2

B

Question. The curved surface area of a right circular cylinder is 4400 cm2. 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

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

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

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

B

Question. If the volume of a sphere is 4851 cm3, then its surface area is
(a) 693 cm2
(b) 1386 cm2
(c) 2079 cm2
(d) 1039.5 cm2

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

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 cm2
(b) 154 cm2
(c) 38.5 cm2
(d) 115.5 cm2

A

Question. If the surface area of a solid sphere is 1386 cm2, then the total surface area of the solid hemisphere of the same radius is
(a) 693 cm2
(b) 1039.5 cm2
(c) 519.75 cm2
(d) 1559.25 cm2

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

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

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

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

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

A

Question. The curved surface area of a right circular cylinder which just encloses a sphere of radius r is
(a) 2πr2
(b) 4πr2
(c) 8πr2
(d) 6πrr2