The radius of the base of a right circular cone is doubled.

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The radius of the base of a right circular cone is doubled. To keep the volume fixed, the height of the come will be ?

1. half of the previous height
2. one-third of the previous height
3. one-fourth of the previous height
4. 1/√2 times of the previous height

Correct Option: C

In first situation.
Radius = r₁, height = h₁ and volume = v₁

In second situation,
Radius =2r₁, height = h₂ and volume = v₂
In the volume is fixed, then
v₁ = v₂
⇒ (1/3)πr²₁h₁ = (1/3)π(2r₁)²h₂
⇒ h₁ = 4h₂
∴ h₂ = h₁/4
Therefore, height of the the cone will be one-fourth of the previous height.