Olympiad – Class X – Mathematics - Surface Area and Volume

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Question - 1

A cuboidal metal of dimensions 44 cm x 30 cm x 15 cm was melted and cast into a cylinder of height 28 cm. Find its radius.

  • A 20 cm
  • B 15 cm
  • C 10 cm
  • D 18 cm

Question - 2

The length of the longest rod which can be kept inside a rectangular box is 27 cm. If the length and the breadth of the box are 23 cm and 10 cm respectively, find its height.

  • A 8 cm
  • B 10 cm
  • C 12 cm
  • D 14 cm

Question - 3

The volume of a cube is numerically equal to its surface area. What is the length of its side?

  • A 6 units
  • B 8 units
  • C 9 units
  • D 10 units

Question - 4

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

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

Question - 5

The lateral surface area of a cylinder is 176 cm2 and its base area is 38.5 cm2. What is its volume?

  • A 830 cm3
  • B 380 cm3
  • C 308 cm3
  • D 803 cm3

Question - 6

Identify the ratio of lateral surface areas of two cylinders with equal heights.

  • A H: h
  • B R: r
  • C 1: 2
  • D 2: 3

Question - 7

A cone and a hemisphere have equal bases and equal volumes. Identify the ratio of their heights.

  • A 1: 3
  • B 1: 2
  • C 2: 1
  • D 3: 1

Question - 8

The area of the base of a cone is 616 sq cm. Its height is 48 cm. Find its total surface area.

  • A 2816 cm2
  • B 2861 cm2
  • C 2618 cm2
  • D 2681 cm2

Question - 9

From a circle of radius 15 cm, a sector central angle 216° is cut and its bounding radii are joined without overlap so as to form a cone. Find its volume.

  • A 1081.3 cm3
  • B 1071.3 cm3
  • C 1018.3 cm3
  • D 1061.9 cm3

Question - 10

A cylindrical vessel of diameter 9 cm has some water in it. A cylindrical iron piece of diameter 6 cm and height 4.5 cm is dropped in it. After it was completely immersed, what is the rise in the level of water?

  • A 0.8 cm
  • B 0.5 cm
  • C 0.1 cm
  • D 0.3 cm
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