A solid metallic sphere of radius 15 cm is melted and recast into a cone having diameter of the base as 15 cm. What is the height of the cone?

Correct option is D

Given:
Radius of the sphere = 15 cm
Diameter of the cone = 15 cm, so radius of the cone = 7.5 cm
Formula Used:
1. Volume of a sphere: V_sphere = (4/3)πr³
2. Volume of a cone: V_cone = (1/3)πr²h
Since the sphere is melted and recast into the cone, the volume of the sphere is equal to the volume of the cone.
Solution:
Vsphere = (4/3)π(15)³ = 4500π cm³
Vcone = (1/3)π(7.5)²h = (1/3)π × 56.25 × h = 56.25πh/3 cm³
4500π = 56.25πh/3
4500 × 3 = 56.25 × h
13500 = 56.25h
h = 13500 / 56.25
h = 240 cm