10th Standard CBSE - Maths - Surface Areas and Volumes

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Question - 1

If a solid, cone of base radius ‘r’ and height ‘h’ is placed over a solid cylinder having same base radius ‘r’ and height – ‘h’ as that of the cone, then the curved surface area of the shape is \(\pi \left( \sqrt { { h }^{ 2 }+r^{ 2 } } \right) +2\pi rh\) Is it true?

  • A No
  • B Yes
  • C May be
  • D Cannot be determined

Question - 2

A cylinder and a cone are of the same base radius and same height. Find the ratio of the volumes of the cylinder of that of the cone.

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

Question - 3

In the figure, the shape of a solid copper piece (made of two pieces) with dimensions as shown. The face ABCDEFA has uniform cross section. Assume that the angles at A, B, C, D, E and F are right angles. Calculate the volume of the piece.

  • A 840 cm
  • B 880 cm3
  • C 876 cm3
  • D 890 cm3

Question - 4

A toy is in the form of a cone mounted on a hemisphere of common base radius 7 cm. The total height of the toy is 31 cm. Find the total surface area of the toy.

  • A 465
  • B 912
  • C 769
  • D 858

Question - 5

What is the area of a semi–circle of radius 5 cm?

  • A 78.57 cm
  • B 71.42 cm
  • C 63.18 cm
  • D 79.86 cm

Question - 6

If a right angled triangle is revolved about one of the sides containing the right angle it forms a

  • A Right circular cone
  • B Right triangle
  • C Prism
  • D Pyramid

Question - 7

If the radius of the base of a right circular cylinder is halved keeping the height same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is

  • A 1:2
  • B 2:1
  • C 4:1
  • D 1:4

Question - 8

A right circular cylinder of radius r cm and height h cm (h>2r) just enclosed a sphere of diameter

  • A r cm
  • B h cm
  • C 2h cm
  • D 2r cm

Question - 9

If the curved surface area of a right circular cylinder is 1760 cm2 and its radius is 10 cm, then what is its height?

  • A 7 cm
  • B 24 cm
  • C 28 cm
  • D 14 cm

Question - 10

A toy is in the form of a cone mounted on a hemisphere of radius 3.5 cm. If the total height of the toy is 15.5 cm, then its total surface area is

  • A 212.6 cm2
  • B 216.2 cm2
  • C 214.5 cm2
  • D 220.6 cm2
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