Question

In the figure, a tent is in the shape of a cylinder surmounted by a conical top of same diameter. If the height and diameter of cylindrical part are $2.1$ m and $3$ m respectively and the slant height of conical part is $2.8$ m, find the cost of canvas needed to make the tent if the canvas is available at the rate of Rs. $500/$sq. metre. Consider $(\pi =\frac{22}{7})$

Answer 1

Radius of the conical part $=$ radius of cylindrical part $r=$ $\frac{3}{2}$ m

Slant height of the cone $l=2.8$ m

Height of the cylinder, $h=2.1$ m

Canvas needed to make the tent $=$ Curved surface area of the conical part + curved surface area of the cylindrical part.

Curved surface area of conical part $=$ $\pi rl=\frac{22}{7}\times \frac{3}{2}\times 2.8=13.2$

Curved surface area of cylindrical part $=2\pi rh=2\times \frac{22}{7}\times \frac{3}{2}\times 2.1=19.8$

Total surface area $=$ Curved surface area of conical part $+$ Curved surface area of cylindrical part

$=13.2+19.8=33m^2$

Cost of $1m^2$ canvas $=$ Rs. $500$

Cost of $33$ $m^2$ canvas $=33\times 500=16500$

Therefore, it will cost Rs. $16500$ for making such a tent.