The surface area of a sphere of radius 5 cm is five times the curved surface area of a cone of radius 4 cm. Find the height and volume (correct to two decimal places) of the cone.

Explanation

Surface area of sphere`=4pir^2=4pixx5xx5=100picm^2`
curved surface area of cone`=pirlcm^2=4pilcm^2`
`100pi=5(4pi)l`
`l=5cm`
`l^2=h^2+r^2`
`5^2=h^2+4^2`
`h^2=9`
`h=3`
volume of cone `=1/3pir^2h`
`1/3xx22/7xx4xx4xx4xx3=35.2/7=50.29cm^3`