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.$12.50/m^2$. (Take $\pi =\frac{22}{7}$)

Answer 1

Cylindrical Part
Diameter $2r=42m$
Radius, $r=21m$
Height $h=21m$
Conical Plant
Radius, $r=21m$
Height $h_1=49-21=28m$
Slant height, $l=\sqrt{h_1^2+r^2}$
$=\sqrt{{28}^2+{21}^2}=7\sqrt{4^2+3^2}=35m$
Total area of the canvas needed $=$CSA of the cylindrical part $+$ CSA of the conical part
$=2\pi rl+\pi rl=\pi r(2h+l)$
$=\frac{22}{7}\times 21(2\times 21+35)=5082$
Therefore, area of the canvas $=5082m^2$
Now, the cost of the canvas per sq.m $=$ Rs.$12.50$
Thus, the total cost of the canvas $=5082\times 12.5=$Rs. $63525$