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Question

Mathematics Question on Surface Areas and Volumes

Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R)
Assertion (A) : If volumes of two spheres are in the ratio 125:64, then their surface areas will be in the ratio 25:16.
Reason (R) : If volumes of two spheres are V1, V2 and their respective surface areas are S1, S2, then
S1S2=(V1V2)23\frac{S_1}{S_2} =(\frac{V_1}{V_2})^\frac{2}{3}
In the light of the above statements, choose the most appropriate answer from the options given below:

A

Both (A) and (R) are correct and (R) is the correct explanation of (A)

B

Both (A) and (R) are correct but (R) is NOT the correct explanation of (A)

C

(A) is correct but (R) is not correct

D

(A) is not correct but (R) is correct

Answer

Both (A) and (R) are correct and (R) is the correct explanation of (A)

Explanation

Solution

The correct option is(A): Both (A) and (R) are correct and (R) is the correct explanation of (A)