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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 

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

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

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

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

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

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

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

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

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

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

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

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

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)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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