Question

A circus tent is cylindrical to a height of 3 m and conical above it. If its base radius is 52.5 m and the slant height of the conical portion is 53 m, find the area of canvas needed to make the tent.

Answer 1

HI there !!

Height = h = 3 metres

Slant height = l = 53 metres

Radius = r = 52.5 metres

Area of canvas required = C.S.A of cone = πrl
= 22/7 ×52.5 ×53

= 8745 m²

Answer 2

Area of the canvas required to make the tent is equal to $9735\ m^{2}$

Solution:

Height of cylindrical tent = 3 m

Radius of the cylindrical part of cylinder =   52.5 m

Radius of conical part of tent and radius is same.

Slant height of tent = 53 m

To find:  

Area of canvas required to cover tent = Surface area of tent - Surface area of base (cone + cylinder) and top as well.

Surface area of the cylinder = $2 \pi r^{2}+(2 \pi r) h$

In this formula $2 \pi r^{2} =0$ (as it is blocked cannot be covered by canvas)

Surface area of the cone = $\pi r^{2}+\pi r s$

In this formula $\pi r^{2}=0$  (as it is blocked cannot be covered by canvas)

Therefore, Area of canvas required to cover or to make tent is as follows,

$(2 \pi r) h+\pi r s=\pi r(2 h+s)$

$\bold{\pi \times 52.5 \times(2 \times 3+53)=9735\ \mathrm{m}^{2}}$