Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10th

# The height and radius of the cone of which the frustum is a part are h1 units and r1 units respectively. Height of the frustum is h2 units and the radius of the smaller base is r2 units. If h2 : h1 - Mathematics

MCQ

The height and radius of the cone of which the frustum is a part are h1 units and r1 units respectively. Height of the frustum is h2 units and the radius of the smaller base is r2 units. If h2 : h1 = 1 : 2 then r2 : r1 is

• 1 : 3

• 1 : 2

• 2 : 1

• 3 : 1

#### Solution

1 : 2

Explanation;

Hint:

h2 : h1 = 1 : 2

h1 : h2 = 2 : 1

Ratio of their volumes

= 1/3 pi"h"_1 ("r"_1^2 + "r"_2^2 + "r"_1"r"_2) : 1/3pi"h"_2 ("r"_1^2 + "r"_2^2 + "r"_1"r"_2)

= 2(r12 + r22 + r1r2) : 1 (r12 + r22 + r1r2)

Volume is 2 : 1 the ratio of their radius also 2 : 1

r1 : r2 = 2 : 1 But r2 : r1 = 1 : 2

Concept: Volume of Frustum of a Cone
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