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