Question

A tent of height 77 dm is in the form of a right circular cylinder of diameter 36 m and height 44 dm surmounted by a right circular cone. Find the cost of the canvas at Rs. 3.50 per $m^2$.

Answer 1

Given:

Diameter of base = 36 m

Radius of the base (r) = 18 m

Height of the cylinder (h) = 44 dm = 4.4 m

Total height = 77 dm = 7.7 m

Thus height of cone (h) = 7.7 m – 4.4 m = 3.3 m

Slant height (l) = $\sqrt{r^2+h^2}$ = $\sqrt{{18}^2+{3.3}^2}$

= $\sqrt{324+10.89}$ = 18.3 m

Now C.S.A. of tent = C.S.A. of cylinder + C.S.A. of cone

= 2πrH + πrl

= πr (2H + l)

= $\frac{22}{7}$ × 18 ( 2 × 4.4 + 18.3) $m^2$

= $\frac{396}{7}$ × (27.1) $m^2$

= $\frac{10731.6}{7}$ $m^2$

Also cost of 1$m^2$ Canvas = Rs 3.50

Cost of total canvas = Rs 3.50 × $\frac{10731.6}{7}$ = Rs. 5365.80