Volumes Practice Test 1

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Question : 21 of 40

Marks: +1, -0

Two spheres have their surface areas in the ratio 9 : 16. Their volumes are in the ratio of

64 : 27
27 : 64
16 : 27
11 : 27

Solution:

Here,

4πr_1^2 : 4πr_2^2

= 9 : 16 ⇒

r_1^2:r_2^2

= 9 : 16
⇒

(r_1/r_2)^2

=

(3/4)^2

⇒

r_1 : r_2

= 3 : 4
⇒

r_1^3/r_2^3

=

{27}/{64}

⇒

r_1^3 : r_2^3

= 27 : 64
Therefore, ratio of their volumes =

4/3 πr_1^3 : 4/3 πr_2^3

=

r_1^3 : r_2^3

= 27 : 64

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