Question

Question 7
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.)

Answer 1

Radius of cylinder = 2 m, height = 2.1 m and slant height of conical top = 2.8 m
Curved surface area of cylindrical portion
$=2\pi rh$
$=2\pi \times 2\times 2.1$
$=8.4\pi m^2$
Curved surface area of conical portion
$=\pi rl$
$=\pi \times 2\times 2.8$
$=5.6\pi m^2$
Total curved surface area
$8.4\pi +5.6\pi =14\pi$
$=14\times \frac{22}{7}=44m^2$
Cost of canvas = Rate $\times$ Surface area
$=500\times 44=Rs.22000$