The volume of a right circular cone, whose radius of the base is half of its altitude, and the volume of a hemisphere are equal. The ratio of the radius of the cone to the radius of the hemisphere is:

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Question

This question was previously asked in

RRB ALP Previous Paper 12 (Held On: 20 Aug 2018 Shift 1)

Answer 1

Let the radius of the cone be r₁and the radius of the hemisphere be r₂,

The radius of the base is half of its altitude,

⇒ r₁= h/2

Volume of the cone = Volume of the hemisphere

⇒ (1/3)πr₁²h = (2/3)πr₂³

⇒ (1/3) h³/4 = (2/3)r₂³

⇒ r₂³ = h³/8

Taking cube root on both sides we get,

⇒ r2 = h/2

We know for cone,

⇒ r₁ = h/2

So, r1 = r₂

∴ r₁/r₂= 1 : 1

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