#### Question

A tent consists of a frustum of a cone capped by a cone. If the radii of the ends of the frustum be 13 m and 7 m , the height of the frustum be 8 m and the slant height of the conical cap be 12 m, find the canvas required for the tent. (Take : π = 22/7)

#### Solution

The height of the frustum cone is h= 8 m. The radii of the end circles of the frustum are r_{1} = 13m and r_{2} =7m.

The slant height of the frustum cone is

`l=sqrt((r_1-r_2)^2+h^2`

`=sqrt((13-7)^2+8^2`

`=sqrt(100)`

= 10 meter

The curved surface area of the frustum is

`S_1=pi(r_1+r_2)xxl`

= π x (13+7) x 10

= π 20 x 10

= 200π m^{2}

The base-radius of the upper cap cone is 7m and the slant height is 12m. Therefore, the curved surface area of the upper cap cone is

S_{2 }= π x 7 x 12

`=22/7xx7xx12`

= 22 x 12

= 264 m^{2}

Hence, the total canvas required for the tent is

S_{1} + S_{2} = 200π + 264

= 892.57 m^{2}

Hence total canvas is 892.57 m^{2}