SURFACE AREAS AND VOLUMES Test

SURFACE AREAS AND VOLUMES

This is SURFACE AREAS AND VOLUMES Test-04 for CBSE class 10 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
A cubical block of side 7 cm is surmounted by a hemisphere. The greatest diameter of the hemisphere is
  • A
    3.5cm
  • B
    7cm
    Correct
  • C
    10.5cm
  • D
    14cm
2
A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1cm and the height of the cone is equal to its radius. The volume of the solid is
  • A
    \(4\pi {\text{ }}c{m^3}\)
  • B
    \(2\pi {\text{ }}c{m^3}\)
  • C
    \(3\pi {\text{ }}c{m^3}\)
  • D
    \(\pi {\text{ }}c{m^3}\)
    Correct
3
The number of silver coins 1.75cm in diameter and of thickness 2mm must be melted to form a cuboid 5.5cm × 10cm × 3.5cm is
  • A
    100
  • B
    400
    Correct
  • C
    300
  • D
    200
4
A hollow sphere of external and internal diameters 8cm and 4cm respectively is melted into a cone of base diameter 8cm. The height of the cone is
  • A
    13cm
  • B
    14cm
    Correct
  • C
    12cm
  • D
    15cm
5
A frustum of a cone is of height 12cm with radii of its circular ends as 2cm and 4cm. The volume of the frustum is
  • A
    \(352c{m^3}\)
    Correct
  • B
    \(354c{m^3}\)
  • C
    \(350c{m^3}\)
  • D
    none of these
6
The CSA of the frustum of a cone is given by
  • A
    \(\pi l({r_1} - {r_2})\) sq. units
  • B
    \(\pi ({r_1} + {r_2})\) sq. units
  • C
    \(\pi l({r_1} + {r_2})\) sq. units
    Correct
  • D
    \(\pi ({r_1} - {r_2})\) sq. units
7
A funnel is the combination of
  • A
    a cone and a hemisphere
  • B
    a hemisphere and a cylinder
  • C
    a cone and a cylinder
  • D
    a frustum of a cone and a cylinder
    Correct
8
The volume of the frustum of a cone is given by
  • A
    \(\frac{1}{3}\pi h({r_1}^2 - {r_2}^2 - {r_1}{r_2}){\text{ }}c{m^3}\)
  • B
    \(\frac{1}{3}\pi h({r_1}^2 + {r_2}^2 - {r_1}{r_2}){\text{ }}c{m^3}\)
  • C
    \(\frac{1}{3}\pi h({r_1}^2 - {r_2}^2 + {r_1}{r_2}){\text{ }}c{m^3}\)
  • D
    \(\frac{1}{3}\pi h({r_1}^2 + {r_2}^2 + {r_1}{r_2}){\text{ }}c{m^3}\)
    Correct
9
The shape of a glass tumbler is usually in the form of
  • A
    a sphere
  • B
    frustum of a cone
    Correct
  • C
    a cylinder
  • D
    a cone
10
A cone is cut through a plane parallel to its base and the small cone is (upper part) removed. The part that is left over is called
  • A
    sphere
  • B
    cylinder
  • C
    cone
  • D
    frustum of a cone
    Correct
11
Frustum is a _______ word
  • A
    Latin
    Correct
  • B
    English
  • C
    none of these
  • D
    Greek
12
The slant height of the frustum of a cone is given by
  • A
    \(\sqrt {{h^2} + {{(R - r)}^2}} \)
    Correct
  • B
    \(\sqrt {{h^2} - {{(R - r)}^2}} \)
  • C
    \(\sqrt {{h^3} + {{(R - r)}^3}} \)
  • D
    \(\sqrt {{h^2} + {{(R + r)}^2}} \)
13
The perpendicular distance between the two parallel circular bases, is called the ______ of the frustum of the cone.
  • A
    radius
  • B
    slant height
  • C
    height
    Correct
  • D
    volume
14
A cone of radius 20 cm is divided into two parts by drawing a plane through the mid-point of its axis parallel to the base. The ratio of the volumes of two parts is
  • A
    1 : 4
  • B
    1 : 2
  • C
    1 : 7
    Correct
  • D
    1 : 3
15
If a cone of radius 10 cm is cut into two parts by a horizontal plane passing through the mid-point of the axis, then the ratio of the volumes of the small cone to that of the original cone is
  • A
    1 : 7
  • B
    1 : 4
  • C
    1 : 2
  • D
    1 : 8
    Correct