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A spherical shaped metal of radius 21 cm is melted and recast into a cone with diameter of the base as 42 cm. What is the height (in cm) of the cone?
1. 63 cm
2. 21 cm
3. 48 cm
4. 84 cm

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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.

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