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## Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 7 Mensuration Ex 7.5

Multiple choice questions.

Question 1.

The curved surface area of a right circular cone of height 15 cm and base diameter 16 cm is ______

(1) 60π cm^{2}

(2) 68π cm^{2}

(3) 120π cm^{2}

(4) 136π cm^{2}

Answer:

(4) 136π cm^{2}

Hint:

Question 2.

If two solid hemispheres of same base radius r units are joined together along with their bases, then the curved surface area of this new solid is

(1) 4πr^{2} sq. units

(2) 67πr^{2} sq. units

(3) 3πr^{2} sq. units

(4) 8πr^{2} sq. units

Solution:

(1) 47πr^{2} sq. units]

Question 3.

The height of a right circular cone whose radius is 5 cm and slant height is 13 cm will be __________

(1) 12 cm

(2) 10 cm

(3) 13 cm

(4) 5 cm

Answer:

(1) 12 cm

Hint:

Question 4.

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

(1) 1 : 2

(2) 1 : 4

(3) 1 : 6

(4) 1 : 8

Solution:

(2) 1 : 4

Question 5.

The total surface area of a cylinder whose radius is \(\frac{1}{3}\) of its height is

Solution:

(3) \(\frac{8 \pi h^{2}}{9}\) sq. units

Question 6.

In a hollow cylinder, the sum of the external and internal radii is 14 cm and the width is 4 cm. If its height is 20 cm, the volume of the material in it is _______

(1) 560π cm^{3}

(2) 1120π cm^{3}

(3) 56π cm^{3}

(4) 360π cm^{3}

Answer:

(2) 1120π cm^{3}

Hint:

R + r = 14 cm

w = 4 cm

h = 90 cm

Question 7.

If the radius of the base of a cone is tripled and the height is doubled then the volume is

(1) made 6 times

(2) made 18 times

(3) made 12 times

(4) unchanged

Solution:

(2) made 18 times

Hint:

Question 8.

The total surface area of a hemisphere is how many times the square of its radius ______

(1) π

(2) 4π

(3) 3π

(4) 2π

Answer:

(3) 3π

Hint:

Question 9.

A solid sphere of radius x cm is melted and cast into a shape of a solid cone of same radius. The height of the cone is

(1) 3x cm

(2) x cm

(3) 4x cm

(4) 2x cm

Solution:

(3) 4x cm

Hint:

Question 10.

A frustum of a right circular cone is of height 16 cm with radii of its ends as 8 cm and 20 cm. Then, the volume of the frustum is _______

(1) 3328π cm3

(2) 3228π cm3

(3) 3240π cm3

(4) 3340π cm3

Answer:

(1) 3328π cm3Hint:

Question 11.

A shuttlecock used for playing badminton has the shape of the combination of

(1) a cylinder and a sphere

(2) a hemisphere and a cone

(3) a sphere and a cone

(4) frustum of a cone and a hemisphere

Solution:

(4) frustum of a cone and a hemisphere

Question 12.

A spherical ball of radius r_{1} units is melted to make 8 new identical balls each of radius r_{2} units. Then r_{1} : r_{2} is

(1) 2 : 1

(2) 1 : 2

(3) 4 : 1

(4) 1 : 4

Solution:

Hint:

Question 13.

The volume (in cm^{3}) of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is

Solution:

(1) \(\frac{4}{3} \pi\)

Question 14.

The height and radius of the cone of which the frustum is a part are h_{1} units and r_{1} units respectively. Height of the frustum is h_{2} units and the radius of the smaller base is r_{2} units. If h_{2}: h_{1} = 1 : 2 then r_{2} : r_{1} is

(1) 1 : 3

(2) 1 : 2

(3) 2 : 1

(4) 3 : 1

Solution:

(2) 1 : 2

Question 15.

The ratio of the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same height is ____

(1) 1 : 2 : 3

(2) 2 : 1 : 3

(3) 1 : 3 : 2

(4) 3 : 1 : 2

Answer:

(4) 3 : 1 : 2

Hint: