Question

Two identical solid hemispheres are kept in contact to form a sphere. The ratio of the total surface areas of the two hemispheres to the surface area of the sphere formed is:

Options

• 1 : 1

• 3 : 2

• 2 : 3

• 2 : 1

Answer 1

3 : 2

Explanation:

Let the common radius be r.

Total surface area of one solid hemisphere

= Curved area + Base 

= 2πr² + πr²

= 3πr²

So, two hemispheres

= 2 × 3πr²

= 6πr²

Surface area of the sphere formed = 4πr².

Ratio = 6πr² : 4πr²

= 6 : 4 

= 3 : 2