A solid is in the form of cone with hemispherical base. The radius of the cone is 15 cm and the total height of the solid is 55 cm. Find the volume of the solid. (π = 3.14)

Given.

A solid is made by mounting a cone onto a hemisphere

The radius of the cone and a hemisphere is 15 cm.

The total height of the solid is 55 cm

Formula used/Theory.

Volume of Cone = πr²h

Volume of hemisphere = πr³

⇒ as we put Cone on hemisphere

The circle part of both cone and hemisphere will attach

∴ Volume of Solid is sum of volume of both cone and hemisphere

Volume of solid = Volume of cone + Volume of Hemisphere

= πr²h + πr³

= πr²[h + 2r]

As height of hemisphere is equal to radius of hemisphere

Then;

Height of cone = Height of Solid – Radius

= 55cm – 15cm

= 40 cm

Volume of solid = × 3.14 × 15 × 15 × [40 + 2 × 15]

= × 15 × 15 × [40 + 30]

= × 5 × 15 × 70

= 22 × 5 × 15 × 10

= 16500 cm³