Question

A toy is in the form of a hemisphere surmounted by a right circular cone of the same base radius as that of the hemisphere. If the radius of the base of the cone is 21 cm and its volume is 2/3 of the volume of hemisphere, calculate the height of the cone and the surface area of the toy.
(Use $\mathrm{\pi }=22/7$).

Answer 1

Solution:

Let the height of the conical part be h.

Radius of the cone = Radius of the hemisphere = r = 21 cm

The toy can be diagrammatically represented as

Volume of the cone =

Volume of the hemisphere =

According to given information:

Volume of the cone × Volume of the hemisphere

Thus, surface area of the toy = Curved surface area of cone + Curved surface area of hemisphere