Correct Answer - Option 4 : 84 cm
Given:
A spherical shaped metal of radius 21 cm is melted and recast into a cone with a diameter of the base as 42 cm.
Formula used:
The volume of a sphere = (4/3)πR3
The volume of a cone = (1/3)πr2h
Where R → The radius of the sphere
r → The radius of the cone
h → The height of the cone
Calculations:
The radius of the sphere (R) = 21 cm
The radius of the cone (r) = 42/2 = 21 cm
According to question,
(4/3)πR3 = (1/3)πr2h
⇒ 4 × 21 × 21 × 21 = 21 × 21 × h
⇒ h = 84 cm
∴ The height of the cone is 84 cm.