Question

A solid sphere is cut into two hemispheres. The ratio of the surface areas of sphere to that of two hemispheres taken together, is ______.

Options

• 1 : 1

• 1 : 4

• 2 : 3

• 3 : 2

Answer 1

A solid sphere is cut into two hemispheres. The ratio of the surface areas of sphere to that of two hemispheres taken together, is 2 : 3.

Explanation:

The total surface area of a sphere = 4πr²

The surface area of one hemisphere = 3πr²

∴ The total surface area of two hemi-sphere = 6πr²

Required Ratio = `(4pir^2)/(6pir^2) = 4/6 = 2/3`