A sphere has a radius of 8 cm. A solid cylinder has a base radius of 4 cm and a height of h cm. If the total surface area of the cylinder is half the surface area of the sphere, then find the height of the cylinder.

Question

Question

This question was previously asked in

RRB NTPC CBT 2 Level -4 Official paper (Held On: 10 May 2022 Shift 1)

Answer 1

Given:

Radius of sphere = 8 cm

Radius of cylinder = 4 cm

The total surface area of the cylinder is half the surface area of the sphere

Formula used:

Total surface area of cylinder = 2πr(h + r)

Surface area of sphere = 4πr²

Calculation:

According to the question

The total surface area of the cylinder is half the surface area of the sphere

⇒ 2πr(h + r)/4πr² = 1/2

⇒ 2 × π × 4(h + 4)/(4 × π × 8²) = 1/2

⇒ 8(h + 4)/256 = 1/2

⇒ h + 4/32 = 1/2

⇒ h + 4 = 16

⇒ h = (16 – 4)

⇒ h = 12 cm

∴ The height of the cylinder is 12 cm

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