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Question

The volumes of the two spheres are in the ratio 64:27. Find the ratio of their surface areas.

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Solution

Let the radius of two spheres be r1 and r2.
Given, the ratio of the volume of two spheres =64:27

V1V2=6427

43πr3143πr32=6427 [ volume of sphere =43πr3]

(r1r2)3=(43)3

r1r2=43

Let the surface areas of the two spheres be S1 and S2.

S1S2=4πr214πr22=(r1r2)2 [ Surface area of sphere =4πr2]

S1:S2=(43)2=169

S1:S2=16:9

Hence, the ratio of their surface areas is 16:9.


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