Question

A solid toy is in the form of a hemisphere surmounted by a right circular cone of height 2 cm and diameter of base 4 cm. If a right circular cylinder circumscribes the toy, find the difference of the volumes of the cylinder and the toy. [Use π = 3.14]

Answer 1

Volume of toy = `"Vol"_"Hemi-sphere" + "Vol"_"Cone"`

= `2/3 πr^3 + 1/3 πr^2h`

= `1/3 πr^2(2r + h)`

= 25.12 cm³

Volume of circumscribing cylinder = πr²H = 50.24 cm³

Now, difference in the volumes of circumscribing cylinder and the toy

= Volume of cylinder – Volume of toy

= (50.24 – 25.12) cm³

= 25.12 cm³

Hence, difference in the volumes of circumscribing cylinder and the toy is 25.12cm³.