SSC CGL 2022 PYQ — Question 66

The correct answer is option 4 i.e. 208 cm

Given:

A solid metallic sphere of radius 13 cm is melted and recast into a cone having a diameter of the base of 13 cm.

Concept used:

The volume of a cone = 1/3πr²h

The volume of a sphere = 4/3πr³

Calculation:

According to the question,

4/3πr³ = 1/3πr²h

Let the height of the cone be h

So,

4 × 13³ = (13/2)² × h 

⇒ h = 4 × 13³ × (2/13)²

⇒ h = 16 × 13

⇒ h = 208

So, height = 208 cm