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The surface area of two spheres are in the ratio 9 : 16. Their volumes will be in the ratio

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The surface area of two spheres are in the ratio 9 : 16. Their volumes will be in the ratio
1). 3 : 64
2). 9 : 27
3). 27 : 64
4). 64 : 729


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Answered by on | Votes 2 |

Surface area of a sphere = 4πr2

Volume of a sphere $(= \frac{4}{3}\pi {r^3})$

Ratio of surface area = (ratio of radius)2

Given, surface area of two spheres are in the ratio 9 : 16.

⇒ ratio of radius = 3 : 4

Ratio of volumes = (ratio of radius)3

⇒ Ratio of volumes $(= {\left( {\frac{3}{4}} \right)^3} = 27:64)$

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