Question

A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are $2.1$ m and $4$ m respectively, and the slant height of the top is $2.8$ m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of Rs $500$ per $m^2$. (Note that the base of the tent will not be covered with canvas.) (Use $\pi =\frac{22}{7}$).

Answer 1

Given:
Height (h) of the cylindrical part = $2.1$ m
Diameter of the cylindrical part = $4$ m
Radius of the cylindrical part = $2$ m
Slant height (l) of conical part = $2.8$ m

Area of canvas used = CSA of conical part + CSA of cylindrical part

$=\pi rl+2\pi rh$

$=\pi \times 2\times 2.8+2\pi \times 2\times 2.1$
$=2\pi [2.8+4.2]$

$=2\times \frac{22}{7}\times 7$

$=44m^2$

Cost of $1$ m ${}^2$ canvas $=500$ rupees
Cost of $44$ m ${}^2$ canvas $=44\times 500=22000$ rupees.

Therefore, it will cost $22000$ rupees for making such a tent.