A metallic sphere of diameter 5.2 cm is melted and recast into a cylinder of radius 5.2 cm. Find the height of the cylinder.

Question

Question

This question was previously asked in

Kerala PSC Common Preliminary Exam (GRADUATE LEVEL) PYP - 096/21

Answer 1

Given:

Diameter of metallic sphere = 5.2 cm

Radius of metallic sphere \((r)\) = 5.2 ÷ 2 = 2.6 cm

Radius of cylinder = 5.2 cm

Formula used:

Volume of sphere = \(\frac{4}{3}\pi r^3\)

Volume of cylinder = \(\pi r^2 h\)

Since the sphere is melted and recast into a cylinder, Volume of sphere = Volume of cylinder

Calculation:

\(\frac{4}{3}\pi r^3 = \pi r^2 h\)

⇒ \(\frac{4}{3} × (2.6)^3 = (5.2)^2 × h\)

⇒ \(\frac{4}{3} × 2.6 = 2\times 2 × h\)

⇒ h = 2.6/3 cm

∴ The correct answer is option (4).

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