Volumes MCQs for Entry Test with Answers and Explanations [PDF]

If the volume and surface area of a sphere is numerically the same then it’s radius is_________?

Option A: 1 unit

Option B: 2 units

Option C: 3 units

Option D: 4 units

Correct Answer: 3 units ✔

Click for More Details

A right cylinder and a right circular cone have the same radius and the same volume. The ratio of the height of the cylinder to that of the cone is_________?

Option A: 3: 5

Option B: 2: 5

Option C: 3: 1

Option D: 1: 3

Correct Answer: 1: 3 ✔

Click for More Details

The radius of a circular cylinder is the same as that of a sphere. Their volumes are equal. The height of the cylinder is________?

Option A: 4/3 times its radius

Option B: 2/3 times its radius

Option C: Equal to it’s radius

Option D: Equal to it’s diameter

Correct Answer: 4/3 times its radius ✔

Click for More Details

The number of solid spheres each of diameter 6 cm, that could be moulded to form a solid metal cylinder of height 45 cm and diameter 4 cm is?

Option A: 3

Option B: 4

Option C: 5

Option D: 6

Correct Answer: 5 ✔

Click for More Details

The length of the wire of 0.2mm radius that can be drawn after melting a solid copper sphere of diameter 18cm?

Option A: 24.3 m

Option B: 243 m

Option C: 2430 m

Option D: 24300 m

Correct Answer: 24300 m ✔

Click for More Details

The radius of a wire is decreased to one –third if volume remains the same length will increase

Option A: 1 Time

Option B: 3 times

Option C: 6 times

Option D: 9 times

Correct Answer: 9 times ✔

Click for More Details

If the volumes of two cubes are in the ratio 8: 1, the ratio of their edges is_________?

Option A: 8: 1

Option B: 2√2 : 1

Option C: 2 : 1

Option D: None of these

Correct Answer: 2 : 1 ✔

Click for More Details

A metal sheet 27 cm long 8cm broad and 1 cm thick is melted into a cube. The difference between the surface areas of two solids is__________?

Option A: 284 cm2

Option B: 286 cm2

Option C: 296 cm2

Option D: 300 cm2

Correct Answer: B. 286 cm² ✔

Click for More Details

A wooden box of dimensions 8m x 7m x 6m is to carry rectangular boxes of dimensions 8cm x 7cm x 6cm. The maximum number of boxes that can be carried in 1 wooden box is?

Option A: 1200000

Option B: 1000000

Option C: 9800000

Option D: 7500000

Correct Answer: 1000000 ✔

Click for More Details

If the length, breadth and the height of a cuboid are in the ratio 6: 5: 4 and if the total surface area is 33300 cm², then length breadth and height in cms, are respectively?

Option A: 90, 85, 60

Option B: 85, 75, 60

Option C: 90, 75, 70

Option D: 90, 75,60

Correct Answer: 90, 75,60 ✔

Click for More Details

The surface area of a cube is 726m², its volume is?

Option A: 1300 m3

Option B: 1331 m3

Option C: 1452 m3

Option D: 1542 m3

Correct Answer: B. 1331 m³ ✔

Click for More Details

The height of two right circular cones are in the ratio 1:2 and their perimeters of their bases are in the ratio 3:4, the ratio of their volume is_________?

Option A: 3:8

Option B: 9:16

Option C: 9:32

Option D: 9:64

Correct Answer: 9:32 ✔

Click for More Details

Surface area of two spheres are in the ratio 1:4 what is the ratio of their volumes?

Option A: 1:64

Option B: 1:8

Option C: 1:4

Option D: 8:1

Correct Answer: 1:8 ✔

Click for More Details

The diameters of two spheres are in the ratio 1:2 what is the ratio of their volumes?

Option A: 3:4

Option B: 9:16

Option C: 1:8

Option D: 4:3

Correct Answer: 1:8 ✔

Click for More Details

The diameters of two spheres are in the ratio 1:2 what is the ratio of their surface area?

Option A: 1:2

Option B: 1:4

Option C: 2:1

Option D: 4:1

Correct Answer: 1:4 ✔

Click for More Details

The sides of a cube are in the ratio 1:2 the ratio of their volume is__________?

Option A: 1:2

Option B: 1:4

Option C: 1:8

Option D: 2:1

Correct Answer: 1:8 ✔

Click for More Details

A rectangular field 30 m long and 20 m broad. How much deep it should be dug so that from the earth taken out, a platform can be formed which is 8 m long, 5.5 m broad and 1.5 m high where as the earth taken out is increase by 10/5?

Option A: 12 cm

Option B: 10 cm

Option C: 18 cm

Option D: 24 cm

Correct Answer: 10 cm ✔

Click for More Details

Calculate the number of bricks, each measuring 25 cm * 15 cm * 8 cm required to construct a wall of dimensions 10 m * 4 m * 5 m when 10% of its volume is occupied by mortar?

Option A: 4000

Option B: 5000

Option C: 6000

Option D: 7000

Correct Answer: 6000 ✔

Click for More Details

If in a box of dimensions 6 m * 5 m * 4 m smaller boxes of dimensions 60 cm * 50 cm * 40 cm are kept in it, then what will be the maximum number of the small boxes that can be kept in it?

Option A: 500

Option B: 1000

Option C: 900

Option D: 600

Correct Answer: 1000 ✔

Click for More Details

A brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 25 m * 2 m * 0.75 m?

Option A: 24000

Option B: 23000

Option C: 22000

Option D: 25000

Correct Answer: 25000 ✔

Click for More Details

In digging a pond 20 m * 10 m * 5 m the volumes of the soil extracted will be_________?

Option A: 100 cu.m

Option B: 1000 cu.m

Option C: 10000 cu.m

Option D: 2000 cu.m

Correct Answer: 1000 cu.m ✔

Click for More Details

If the height of a cone is increased by 100% then its volume is increased by_________?

Option A: 100%

Option B: 200%

Option C: 300%

Option D: 400%

Correct Answer: 100% ✔

Click for More Details

A cylinder and a cone have a same height and same radius of the base. The ratio between the volumes of the cylinder and cone is__________?

Option A: 1:3

Option B: 3:1

Option C: 1:2

Option D: 2:1

Correct Answer: 3:1 ✔

Click for More Details

The length of the longest rod that can fit in a cubical room of 4 m side is?

Option A: 8.66 m

Option B: 5.196 m

Option C: 6.928 m

Option D: 7.264 m

Correct Answer: 6.928 m ✔

Click for More Details

The area of the cardboard(in cm²) needed to make a box of size 25 cm * 15 cm * 8 cm will be__________?

Option A: 1390 cm2

Option B: 695 cm2

Option C: 1280 cm2

Option D: 1220 cm2

Correct Answer: A. 1390 cm² ✔

Click for More Details

A tank 3 m long, 2 m wide and 1.5 m deep is dug in a field 20 m long and 14 m wide. If the earth dug out is evenly spread out over the field, the level of the field will raise by nearly?

Option A: 0.299 cm

Option B: 0.29 cm

Option C: 2.98 cm

Option D: 4.15 cm

Correct Answer: 2.98 cm ✔

Click for More Details

A river 2m deep and 45 m wide is flowing at the rate of 3 kmph the amount of water that runs into the sea per minute is?

Option A: 4500 M3

Option B: 27000 M3

Option C: 3000 M3

Option D: 2700 M3

Correct Answer: A. 4500 M³ ✔

Click for More Details

The dimensions of an open box are 52, 40 and 29 cms. Its thickness is 2 cms. If 1 cm³ of metal used in the box weighs 0.5 gms, the weight of the box is________?

Option A: 8.56 kg

Option B: 7.76 kg

Option C: 7.756 kg

Option D: 6.832 kg

Correct Answer: 6.832 kg ✔

Click for More Details

The ratio of the volumes of a cube to that of the sphere which will fit inside the cube is________?

Option A: 4:3

Option B: 4:2

Option C: 4:4

Option D: 6: π

Correct Answer: 6: π ✔

Click for More Details

A room is 15m long, 4m broad and 3m height. Find the cost of white washing its four walls at 50p per m²?

Option A: Rs.60

Option B: Rs.57

Option C: Rs.55

Option D: Rs.52

Correct Answer: Rs.57 ✔

Click for More Details

How many meters of carpet 50cm, wide will be required to cover the floor of a room 30m * 20m?

Option A: 1000

Option B: 600

Option C: 2400

Option D: 1200

Correct Answer: 1200 ✔

Click for More Details

A rectangular courtyard, the sides of which are in the ratio of 4:3, cost Rs.600 for paving at 50 p per m²; find the length of the diagonal of the courtyard?

Option A: 25 m

Option B: 35 m

Option C: 45 m

Option D: 50 m

Correct Answer: 50 m ✔

Click for More Details

If the sides of a cube are in the ratio 4:3. What is the ratio of their diagonals?

Option A: 4:3

Option B: 16:9

Option C: 64:27

Option D: 3:4

Correct Answer: 4:3 ✔

Click for More Details

Three cubes of metal whose edges are 9, 12 and 15 cm respectively, are melted and one new cube is made. Find the edge of the new cube?

Option A: 21 cm

Option B: 19 cm

Option C: 32 cm

Option D: 18 cm

Correct Answer: 18 cm ✔

Click for More Details

The ratio between the radii of two spheres is 1:3. Find the ratio between their volumes?

Option A: 27:1

Option B: 1:27

Option C: 1:9

Option D: 9:1

Correct Answer: 1:27 ✔

Click for More Details

How many shots of 1cm radius can be prepared from a sphere of 3cm radius?

Option A: 36

Option B: 64

Option C: 27

Option D: 16

Correct Answer: 27 ✔

Click for More Details

Find the ratio between whole surfaces of a sphere and a hemisphere?

Option A: 3:4

Option B: 4:3

Option C: 3:1

Option D: 1:3

Correct Answer: 4:3 ✔

Click for More Details

The curved surface of a sphere is 64 π cm². Find its radius?

Option A: 1 cm

Option B: 2 cm

Option C: 4 cm

Option D: 3 cm

Correct Answer: 4 cm ✔

Click for More Details

The slant height of a cone is 12 cm and radius of the base is 4cm, find the curved surface of the cone.

Option A: 74 π cm2

Option B: 36 π cm2

Option C: 48 π cm2

Option D: 24 π cm2

Correct Answer: C. 48 π cm² ✔

Click for More Details

The area of a base of a cone is 30 cm². If the height of the cone is 6cm, find its volume?

Option A: 120 cm3

Option B: 40 cm3

Option C: 50 cm3

Option D: 60 cm3

Correct Answer: D. 60 cm³ ✔

Click for More Details

The radius of the base of cone is 3 cm and height is 4 cm. Find the volume of the cone?

Option A: 12 π cm3

Option B: 6 π cm3

Option C: 8 π cm3

Option D: 10 π cm3

Correct Answer: A. 12 π cm³ ✔

Click for More Details

Find the ratio of the curved surfaces of two cylinders of same heights if their radii are in the ratio 1:2.

Option A: 1:2

Option B: 2:1

Option C: 1:4

Option D: 4:1

Correct Answer: 1:2 ✔

Click for More Details

Two cylinders are of the same height. Their radii are in the ratio 1: 3. If the volume of the first cylinder is 40 cc. Find the volume of the second cylinder?

Option A: 360 cc

Option B: 60 cc

Option C: 300 cc

Option D: 36 cc

Correct Answer: 360 cc ✔

Click for More Details

Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.15 per cubic meter?

Option A: Rs.1185

Option B: Rs.1285

Option C: Rs.1385

Option D: Rs.1485

Correct Answer: Rs.1485 ✔

Click for More Details

The radius of a cylindrical vessel is 7cm and height is 3cm. Find the whole surface of the cylinder?

Option A: 308 sq cm

Option B: 220 sq cm

Option C: 440 sq cm

Option D: 132 sq cm

Correct Answer: 440 sq cm ✔

Click for More Details

The diameter of a cylindrical tin is 6cm and height is 5 cm. Find the volume of the cylinder?

Option A: 30 π cc

Option B: 45 π cc

Option C: 150 π cc

Option D: 180 π cc

Correct Answer: 45 π cc ✔

Click for More Details

The radius of a cylinder is 2 r units and height is 3 r units. Find the curved surface?

Option A: 18 πr2 sq units

Option B: 3 πr2 sq units

Option C: 12 πr2 sq units

Option D: 6 πr2 sq units

Correct Answer: C. 12 πr² sq units ✔

Click for More Details

The spherical ball of lead 3 cm in diameter is melted and recast into 3 spherical balls. The diameters of two of these are 1 ½ cm and 2 cm respectively. The diameter of third ball is?

Option A: 2.66 cm

Option B: 2.5 cm

Option C: 3 cm

Option D: 3.5 cm

Correct Answer: 2.5 cm ✔

Click for More Details

If a solid sphere of radius 10 cms is moulded into 8 spherical solid balls of equal radius, then surface area of each ball (in cm²) is________?

Option A: 100π

Option B: 7π

Option C: 60π

Option D: 50π

Correct Answer: 100π ✔

Click for More Details

The areas of the two spheres are in the ratio 1: 4. The ratio of their volume is?

Option A: 1:4

Option B: 1:16

Option C: 1:8

Option D: 1:64

Correct Answer: 1:8 ✔

Click for More Details

The volumes of two cubes are in the ratio 27: 125, what shall be the ratio of their surface areas?

Option A: 6:25

Option B: 3:5

Option C: 9:25

Option D: 16:25

Correct Answer: 9:25 ✔

Click for More Details

What is the length of the longest pole which can be kept in a room 12 m long, 4 m broad and 3 m high?

Option A: 10 cm

Option B: 12 cm

Option C: 15 cm

Option D: 13 cm

Correct Answer: 13 cm ✔

Click for More Details

Find the length of the wire required to go 15 times round a square field containing 69696 m².

Option A: 15840 m

Option B: 16840 m

Option C: 15820 m

Option D: 15640 m

Correct Answer: 15840 m ✔

Click for More Details

The edges of three iron cubes are 6cm; 8cm; 10cm respectively. A new cube was made by melting them. Find the edge of the new cube?

Option A: 8 cm

Option B: 12 cm

Option C: 14 cm

Option D: 10 cm

Correct Answer: 12 cm ✔

Click for More Details

The area of the floor of a room is 20 m² that of a longer wall 15 m² and of the shorter wall 12 m², find the edge of the new cube?

Option A: 450 m3

Option B: 100 m2

Option C: 60 m3

Option D: 400 m3

Correct Answer: C. 60 m³ ✔

Click for More Details

If the sides of two cubes are in the ratio 3: 1 the ratio of their total surface area is?

Option A: 3:1

Option B: 8:1

Option C: 9:1

Option D: 12:1

Correct Answer: 9:1 ✔

Click for More Details

The edges of a cuboid are respectively 3cm, 4cm and 12 cm. Find the length of the diagonal of cuboid.

Option A: 5 cm

Option B: 19 cm

Option C: 13 cm

Option D: 144 cm

Correct Answer: 13 cm ✔

Click for More Details

The edges of a cuboid are 4 cm, 5 cm and 6 cm. Find the volume of the cuboid?

Option A: 120 cm3

Option B: 120 cm2

Option C: 148 cm2

Option D: 15 cm3

Correct Answer: B. 120 cm² ✔

Click for More Details

The edges of cuboid are 4 cm; 5 cm and 6 cm. Find its surface area?

Option A: 120 cm2

Option B: 148 cm2

Option C: 74 cm2

Option D: 15 cm2

Correct Answer: B. 148 cm² ✔

Click for More Details

The edge of three cubes of metal is 3 dm, 4 dm and 5 dm. They are melted and formed into a single cube. Find the edge of the new cube?

Option A: 3 dm

Option B: 4 dm

Option C: 5 dm

Option D: 6 dm

Correct Answer: 6 dm ✔

Click for More Details

How many cubes of edge 2 dm can be cut out of a meter cube?

Option A: 50

Option B: 64

Option C: 216

Option D: 125

Correct Answer: 125 ✔

Click for More Details

The volume of a cube is 1728 cc. Find its surface.

Option A: 864 cm2

Option B: 648 cm2

Option C: 486 cm2

Option D: 468 cm2

Correct Answer: A. 864 cm² ✔

Click for More Details

The surface of a cube is 24sq cm. Find its volume?

Option A: 8 cc

Option B: 16 cc

Option C: 32 cc

Option D: 64 cc

Correct Answer: 8 cc ✔

Click for More Details

The edge of a cube is 2a cm. Find its surface?

Option A: 6a2 cm2

Option B: 8a2 cm2

Option C: 12a2 cm2

Option D: 24a2 cm2

Correct Answer: D. 24a² cm² ✔

Click for More Details

A solid consists of a circular cylinder with an exact fitting right circular cone placed on the top. The height of the cone is h. If the total volume of the solid is three times the volume of the cone then the height of the cylinder is________?

Option A: 2h

Option B: 4h

Option C: 2h/3

Option D: 3h/2

Correct Answer: 2h ✔

Click for More Details

If the radius of the sphere is doubled then it’s volume is increased by?

Option A: 100 %

Option B: 200 %

Option C: 700 %

Option D: 800 %

Correct Answer: 700 % ✔

Click for More Details

The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the ratio of its diameter to its height.

Option A: 3 : 7

Option B: 7 : 3

Option C: 6 : 7

Option D: 7 : 6

Correct Answer: 7 : 3 ✔

Click for More Details

A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is__________?

Option A: 90 cm

Option B: 1 dm

Option C: 1 m

Option D: 1.1 cm

Correct Answer: 1 dm ✔

Click for More Details

What is the total surface area of a right circular cone of height 14 cm and base radius 7 cm?

Option A: 344.35 cm2

Option B: 344.35 cm2

Option C: 344.35 cm2

Option D: None of these

Correct Answer: 344.35 cm2 ✔

Click for More Details

A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?

Option A: 2 : 1

Option B: 3 : 2

Option C: 25 : 18

Option D: 27 : 20

Correct Answer: 25 : 18 ✔

Click for More Details

Surface area of a sphere is 2464 cm2. If its radius is doubled, then the surface area of _________?the new sphere will be

Option A: 4920 cm2

Option B: 4727 cm2

Option C: 9856 cm2

Option D: 19712 cm2

Correct Answer: 9856 cm2 ✔

Click for More Details