Asolid 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

(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.

5

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