Find the total volume of a cone having a hemispherical base. If the radius of the base is 21 cm and height 60 cm.

Given.

Radius of cone and hemisphere = 21 cm

Total height of cone = 60 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;

Volume of top = × 21 × 21 × [60 + 2 × 21]

= × 21 × 21 × [60 + 42]

= × 21 × 21 × [102]

= 22 × 21 × 102

= 47124 cm³