Question

A circus tent is to be erected in the form of a cone surmounted on a cylinder. The total height of the tent is $49m$. Diameter of the base is $42m$ and height of the cylinder is $21m$. Find the cost of canvas needed to make the tent, if the cost of canvas is Rs. $12.50m^2$. (Take $=\frac{22}{7}$)

Answer 1

Cylinder:
Diameter $=42$ m $\Rightarrow$ Radius $\left(r\right)=21$ m
Height $\left(h\right)=21$ m
C.S.A. Cylinder $=2\pi rh$ square cm
$=2\times \frac{22}{7}\times 21\times 21$
$=2772m^2$
Cone:
Radius $\left(r\right)=21$ m, Height $\left(h\right)=28$ m
$l=\sqrt{4^2+r^2}$
$=\sqrt{{28}^2+{21}^2}$
$=\sqrt{1225}=35$ m
C.S.A. of cone $=\pi rl$ square cm
$=\frac{22}{7}\times 21\times 35=2310m^2$
Total surface area of circus tent
$=2772+2310=5082m^2$
The cost of $1$ square metre $=$ Rs. $12.50$
Total cost of canvas $=5082\times 12.50=$ Rs. $63,525$