The volumes of two spheres are in the ratio of 512 : 3375. The ratio of their surface areas is:
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Correct answer: D
Explanation
The correct answer is Option 4 i.e. 64 : 225.
Volume of a sphere = 4πr3/3
According to the question -
Ratio of volume of two spheres = 512/3375
⇒ [4πr13/3]/[4πr23/3] = 512/3375
⇒ (r1/r2)3 = 512/3375
⇒ r1/r2 = 8/15
Surface area of a sphere = 4πr2
Ratio of surface area of two spheres = [4πr12]/[4πr22] = (r1/r2)2 = (8/15)2 = 64/225 = 64 : 225