Question

a circus tent is cylindrical in shape up to a height of 4.2 m and conical above it. the common diameter of the base of the cylindrical and conical parts is 6 m. if the total height of the tent from the ground is 8.2 m, find the cost of canvas needed to make the tent at the rate of Rs.160 per m²

Answer 1

Given circus tent is in the shape of cylinder.
So, height $h_1=4.2m$ and common diameter for both cylinder cone is $6m$
$\Rightarrow r_1=r_2=3m$ as it is half of the diameter.

Height of the cone =$h_2=8.2-4.2=4m$
Slant height $=l=\sqrt{4^2+3^2}$
$\therefore l=\sqrt{16+9}=\sqrt{25}=5m$
Total surface area = curved surface area of cylinder + curved surface area of cone
$=2\pi r_1{h}_1+\pi r_{2}l$
$=\frac{22}{7}\times 3\left(2\right(4.2)+(5\left)\right)$
$=\frac{22}{7}\times 3(8.4+5)$
$=\frac{22}{7}\times 3\times 13.4$
$=126.34m^2$
Since, the cost of canvas needed to make the tent at the rate of Rs.160 per $m^2$.
Total cost=$126.34\times 160m^2$
$=Rs.20214.86$