Previous Year Questions

Given that, the height of the cone is half of it's diameter.

This means, the height of the cone = the radius of the cone = the radius of hemisphere = x

So, the height of the cylinder = 2x

Vacant part of the cylinder = Volume of cylinder - Volume of vessel

=>πx²(2x) - [(2/3)πx³ + (1/3)πx²x

=>2πx³ - [(2/3)πx³ + (1/3)πx³]

=>2πx³ - πx³

=>πx³

So, the vacant part of the cylinder = πx³/2πx³ = 1/2