A playing top is made up of steel. The top is shaped like a cone surmounted by a hemisphere. The total height of top is 5 cm and the diameter of the top is 3.5 cm. Find the volume of the top.

Given.

Diameter of cone and hemisphere = 3.5cm

Total height of top = 5cm

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 top is sum of volume of both cone and hemisphere

Volume of top = Volume of cone + Volume of Hemisphere

= πr²h + πr³

= πr²[h + 2r]

Radius of hemisphere =

= = 1.75

As height of hemisphere is equal to radius of hemisphere

Then;

Height of cone = Height of top – Radius

= 5cm – 1.75cm

= 3.25 cm

Volume of top = × 1.75 × 1.75 × [3.25 + 2 × 1.75]

= × 1.75 × 1.75 × [3.25 + 3.5]

= × 1.75 × 1.75 × [6.75]

= 22 × 0.25 × 1.75 × 2.25

= 21.65 cm³