Question

The lower part of a tent is cylindrical in shape and its upper part is conical in shape. The diameter of the base of the tent is 20 m. The height of the cylindrical part and conical part are 2.5 m and 7.5 m respectively. Find the canvas required for the tent. Find the cost of the canvas at Rs. 150 per sq.m

Answer 1

Diameter of base of tent = 20 m
Then, radius of base of tent = 10 m
Height of cylindrical part = 2.5 m
Curved surface area of cylindrical part = $2\mathrm{\pi rh}=2\times \frac{22}{7}\times 10\times 2.5=157.14{\mathrm{m}}^2$
Height of conical part = 7.5 m
Then, curved surface area of conical part = $\mathrm{\pi r}\sqrt{{\mathrm{h}}^2+{\mathrm{r}}^2}=\frac{22}{7}\times 10\times \sqrt{7.5^2+{10}^2}=\frac{22}{7}\times 10\times 12.5=392.85{\mathrm{m}}^2$
Total surface area of tent = Curved surface area of cylindrical part + curved surface area of conical part
= $157.14{\mathrm{m}}^2+392.85{\mathrm{m}}^2=549.99\approx 550{\mathrm{m}}^2$
So canvas required for tent is 550 square metre.
Now, cost of canvas per square metre = Rs.150
Therefore, total cost of canvas required = $550\times 150$ = Rs.82500