A right circular metal cone solid is 8 cm high and the radius is 2 cm It is melted and recast into a...........

Quantitative Aptitude ( CCS) Mensuration 3D

A right circular metal cone (solid) is 8 cm high and the radius is 2 cm. It is melted and recast into a sphere. What is the radius of the sphere ?

2 cm

3 cm

4 cm

5 cm

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Explanation:

Given that, height of cone (h) = 8 cm and radius of cone (r) = 2 cm
Let radius of sphere = R
Note : When an object is melted and given a different shape, the volumes of both the objects (of two different shapes) remain equal.
∴ Volume of cone = Volume of sphere
⇒ 1/3πr²h = 4/3πR³
⇒ (2)² × 8 = 4R³
⇒ R³ = 8
∴ R = 2 cm