CLAT - Mathematical Ability - Volume and Surface Area

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Question - 1

The length of the longest pole that can be kept in a room 5 m long, 4 m broad and 3 m high, is:

  • A \(5\sqrt{2}\) m
  • B \(6\sqrt{2}\) m
  • C \(7\sqrt{2}\) m
  • D none of these

Question - 2

A solid metallic sphere of diameter 21 cm is melted and recasted into a number of smaller cones, each of diameter 7 cm and height 3 cm. Find the number of cones so formed.

  • A 503
  • B 502
  • C 501
  • D 504

Question - 3

Find the volume and the surface area of the sphere of radius 5.6 cm.(π=22/7)

  • A 735.9 cm3, 394.2 cm2
  • B 733.0 cm3, 394.3 cm2
  • C 735.2 cm3, 394.4 cm2
  • D 700.9 cm3, 394.2 cm4

Question - 4

The product of the areas of three adjacent faces of a rectangular box is equal to:

  • A the volume of the box
  • B twice the volume of the box
  • C the square of the volume of the box
  • D cube root of the volume of the box

Question - 5

A well with 14 m diameter is dug 8 m deep. The earth taken out of it has been evenly spread all around it to a width of 21 m to form an embankment. Find the height of embankment.

  • A 52.3 m
  • B 53.3 m
  • C 51.3 m
  • D 53 m

Question - 6

The largest sphere is carved out of a cube of side 10 cm. Find the volume of the spheres.

  • A 524.59 cm3
  • B 523.60 cm3
  • C 523.59 cm3
  • D 523.58 cm3

Question - 7

A well with 10 m inside diameter is dug 14 m deep. Earth taken out of it and spread all around to a width of 5 m to form an embankment. Find the height of embankment.

  • A 4.67 m
  • B 4.65 m
  • C 4.64 m
  • D 4.66 m

Question - 8

The diameter of the internal and external surfaces of a hollow spherical shell are 6 cm and 10 cm respectively. If it is melted and recast into a solid cylinder of diameter 14 cm, find the height of the cylinder.

  • A 8/3 cm
  • B 8/2 cm
  • C 7/3 cm
  • D 1/2 cm

Question - 9

Water is being pumped out through a circular pipe whose internal diameter is 7 cm. If the flow of water is 72 cm per second how many litres of water are being pumped out in one hour?

  • A 9979.2 litres
  • B 9980.2 litres
  • C 9979.3 litres
  • D 9879 litres

Question - 10

If the diameter of the cross-section of a wire is decreased by 5%, how much per cent will the length be increased, so that the volume remains the same?

  • A \(\frac{360}{400}\)
  • B \(\frac{363}{400}\)
  • C \(\frac{361}{400}\)
  • D \(\frac{363}{401}\)
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