Question

A water reservoir in the form of a cone mounted on a hemispere is built such that the plane face of the hemisphere is built fits exactly to the base of the cone and the height of the cone is 6 times the radius of its base.

(a) Illustrate this information in a diagram,

(b) If the volume of the reservoir is 3331/3 pi m3 , calculate, correct to the nearest whole number, the:

(i) volume of the hemisphere

(ii) total surface area of the reservoir. (Take pi = 22/7)

Answer 1

Is this physics or geometry?
If the radius of the hemisphere (and cone base) is r, then the volume of the hemisphere + cone is
2/3 π r^3 + 1/3 π r^2 (6r) = 8/3 π r^3
The area is thus 2πr^2 + 2π√37 r^2

You can use your given volume to find r.