SSC CGL 2022 PYQ — Question 53

The correct answer is option 3 i.e. 1.33 cm.

Given:

A hemisphere of lead of radius 4 cm is cast into a right circular cone of height 72 cm.

Concept used:

1. Volume of hemisphere 2π × Radius³

2. Volume of a cone = (π  × Radius²  × Height)/3

3. The volume of the hemisphere must be equal to the volume of the cone.

Calculation:

The volume of the hemisphere = (2π × 4³)/3

= 128π/3 cm³

Let the radius of the base of the right circular cone be R cm.

According to the concept,

 128π/3 cm³ = (π × R × 72)/3

⇒ R² = 16/9

⇒ R = 4/3

⇒ R ≈ 1.33

The radius of the base of the cone is 1.33 cm.