Question

A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 2 cm and the diameter of the base is 4 cm. Determine the volume of the toy.

Answer 1

Given, height of cone (h) = OA = 2 cm and diameter of cone = 4 cm

So, radius = r = `("Diameter")/2`

= `4/2`

= 2 cm

Now, Volume of toy = Volume of cone + Volume of hemisphere

Volume of cone = `1/3πr^2h`

= `1/3 xx 22/7 xx (2)^2 xx 2`

= `176/21  "cm"^3`

and volume of hemisphere = `2/3πr^3`

= `2/3 xx 22/7 xx (2)^3`

= `352/21  "cm"^3`

∴ Volume of toy = `176/21 + 352/21`

= `528/21`

= 25.14 cm³