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.
Answer
We have,
Height of the cylindrical part, $H = 4m$,
Radius of the base, $\text{r}=\frac{105}{2}\text{m}$ and
Slant height of the conical part, $l = 40m$
Now,
The total area of canvas required = CSA of conical part + CSA of cylindrical par
$=\pi\text{r}\text{l}+2\pi\text{r}\text{H}$
$=\pi\text{r}(\text{l}+2\text{H})$
$=\frac{22}{7}\times\frac{105}{2}\times40+2\times4$
$=11\times15\times48$
$=7920\text{m}^2$
So, the area of the canvas required to make the tent is $7920\ m^2$.