Question

A solid consist of a cone and a hemisphere which share common base. the cone has a base radius of 35cm. given that the volume of the cone is equal to 1 1/5 of the volume of the hemisphere find
a) the height of the cone
b)the total surface area of the solid, leaving your answer in terms of pi

Answer 1

Answer:

(i)  84 cm.

(ii)  5635π cm^2

Step-by-step explanation:

(i)

The volume of the cone = 1/3 π r^2 h

= 1/3 π 35^2 h.

The volume of the hemisphere = 2/3 π 35^3.

As the volume of the cone is 1 1/5 ( = 6/5) times the volume of the hemisphere:

1/3 π 35^2 h =  2/3 π 35^3 * 6/5

h =  2/3 π 35^3 * 6/5 /   1/3 π 35^2

h =  84 cm (answer).

(ii)  Surface area of the hemisphere = 2 π * 35^2 =   2450π cm^2.

Surface area of the cone = π r l  where l = slant height.

l = √(35^2 + 84^2) =  91 cm.

So the surface area of the cone =  35*91 π = 3185π.

So the  total surface area of the solid is  3185π + 2450π

= 5635π cm^2.