A sphere and a hemisphere have the same surface area.

Home » Aptitude » Volume and Surface Area of Solid Figures » Question

A sphere and a hemisphere have the same surface area. The ratio of their volumes is ?

1. √3/4 : 1
2. 3√3/4 : 1
3. √3/8 : 1
4. 3√3/8 : 1

Correct Option: D

According to the question,
Surface area of sphere = Surface area of hemisphere
4πr₁² =3πr₂²
⇒ r₁/r₂ = √3/2
∴ Ratio in volume = [(4/3)πr₁³] / [(4/3)πr₂³]
= 3√3/8 : 1