A metallic sphere of radius 4.2 cm is melted and recast into a cylinder of radius 6 cm, then the height of the cylinder is-

Question

Question

This question was previously asked in

Bihar Police Prohibition SI Memory Based Paper (Held on: 16th July 2023)

Answer 1

Given:

The sphere of radius = 4.2 cm

The cylinder of radius = 6 cm

Formula used:

The volume of the sphere = \(\dfrac{4}{3}\)πr³

The volume of the cylinder = πr²h

Calculation:

According to the question, A metallic sphere of radius 4.2 cm is melted and recast into a cylinder of radius 6 cm.

The volume of the sphere = The volume of the cylinder

⇒ \(\dfrac{4}{3}\)πr3 = πr2h

⇒ \(\dfrac{4}{3}\) × (4.2)³ = 6² × h

⇒ h = \(\dfrac{4\times4.2^3}{3\times6^2}\)= 2.74 cm

∴ The height of the cylinder is 2.74 cm.

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