Question

A circus tent is made if canvas and is in the form of a right circular cylinder and a right circular cone above it. The diameter and height of the cylindrical part of the tent are $126$m and $5$m respectively. The total height of the tent is $21$m. Find the total cost of the canvas used to make the tent when the cost per $m^2$ of the canvas is Rs. $15$.

Answer 1

Cylindrical part: $r=\frac{126}{2}=63m,h=21-5=16m$
$l=\sqrt{r^2+h^2}=\sqrt{{63}^2+{16}^2}$
$=\sqrt{3969+256}=\sqrt{4225}$
$\therefore l=65m$
Total canvas used$=$CSA of cylindrical part$+$ CSA of conical part
$=2\pi rh+\pi rl=2\times \frac{22}{7}\times 63\times 5m^2+\frac{22}{7}\times 63\times 65m^2$
$=1980m^2+12870m^2=14850m^2$
$\therefore$ Total canvas used$=14,850m^2$
Cost of canvas at the rate of Rs. $16$per $m^2=14,850\times Rs.15=Rs.2,22,750$
$\therefore$ Cost of canvas$=Rs.2,22,750$.