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 pi = 22/7)`
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 = `1/3pir^2h`
Volume of the hemisphere = `2/3pir^3`
According to given information:
Volume of the cone `=2/3`× Volume of the hemisphere
`therefore h=4/3xx21cm =28 cm`
Thus, surface area of the toy = Curved surface area of cone + Curved surface area of hemisphere
= πrl + 2πr2
= 66(35+42) cm2
= 66 x 77 cm2
= 5082 cm2