Question:
A circus tent is cylindrical to a height of 4 m and conical above it. If its diameter is 105 m and its slant height is 40 m, then find the total area of the canvas required.
Solution:
We have,
Height of the cylindrical part, $H=4 \mathrm{~m}$,
Radius of the base, $r=\frac{105}{2} \mathrm{~m}$ and
Slant height of the conical part, $l=40 \mathrm{~m}$
Now,
The total area of canvas required = CSA of conical part + CSA of cylindrical part
$=\pi r l+2 \pi r H$
$=\pi r(l+2 H)$
$=\frac{22}{7} \times \frac{105}{2} \times(40+2 \times 4)$
$=11 \times 15 \times 48$
$=7920 \mathrm{~m}^{2}$
So, the area of the canvas required to make the tent is 7920 m2.