Question

A solid consists of a circular cylinder with an exact fitting right circular cone placed at the top. The height of the cone is h. If the total volume of the solid is 3 times the volume of the cone, then the height of the circular is

Options

•  2h

• \[\frac{2h}{3}\]

• \[\frac{3h}{2}\]

•  4h

Answer 1

Let r be the radius of the base of solid.

Clearly,

The volume of solid = 3 × volume of cone

Vol. of cone + Vol. of cylinder = 3 Volume of cone

Vol. of cylinder = 2 Vol. of cone

`pir^2 x = 2 xx 1/3 pi r^2 h`

      `x = 2/3 h`

Thus,

The height of cylinder `= (2h)/3`