Olympiad – Class IX – Mathematics - Surface Areas and Volumes

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Question - 1

If volume and surface area of a sphere are numerically equal, find its radius.

  • A 2 units
  • B 3 units
  • C 4 units
  • D 5 units

Question - 2

The base radius of a cylinder is \(1\frac{2}{3}\) times its height. The cost of painting its C.S.A at 2 paise/cm2 is Rs 92.40. What volume of the paint is required?

  • A 80850 cm3
  • B 80580 cm3
  • C 80508 cm3
  • D 85800 cm3

Question - 3

The total surface area of a cylinder of height 6.5 cm is 220 sq cm. Find its volume.

  • A 25.025 cm3
  • B 2.5025 cm3
  • C 2502.5 cm3
  • D 250.25 cm3

Question - 4

The height of a cylinder is 15 cm. The curved surface area is 660 sq. cm. Find its radius. (Take \(\pi\ as \frac{22}{7}\))

  • A 7 cm
  • B 9 cm
  • C 6 cm
  • D 11 cm

Question - 5

A cylindrical vessel contains 49.896 litres of liquid. Cost of painting its C.S.A. at 2 paise/sq cm is Rs 95.04. What is its total surface area?

  • A 5724 cm2
  • B 7524 cm2
  • C 5742 cm2
  • D 7254 cm2

Question - 6

What is the ratio of volumes of two cones with the same radii?

  • A h1: h2
  • B r1:r2
  • C s1:s2
  • D 1:2

Question - 7

What is the length of the longest pole that can be put in a room of dimensions 10 m x 10 m x 5 m?

  • A 15 m
  • B 16 m
  • C 10 m
  • D 12 m

Question - 8

The cost of painting the T.S.A. of cone at 5 ps/cm2 is Rs35.20. Determine the volume of the cone if its slant height is 25 cm.

  • A 1223 cm2
  • B 1232 cm2
  • C 1323 cm2
  • D 1332 cm2

Question - 9

A vessel is conical in shape. If its volume is 33.264 litres and height is 72 cm, what is the cost of repairing its C.S.A. at Rs 12/sq.m?

  • A Rs 5.94
  • B Rs 6.94
  • C Rs 7.95
  • D Rs 7.59

Question - 10

A joker's cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the areas of the sheet required to make 10 such caps.

  • A 5000 cm2
  • B 6200 cm2
  • C 5500 cm2
  • D 6000 cm2