Question

A tent is in the form of a cylinder surmounted by a cone having its diameter of the base equal to 24 m. The height of cylinder is 11 m and the vertex of the cone is 5 m above the cylinder. Find the cost of making the tent, if the rate of canvas is Rs. 10 per m${}^2$.

Answer 1

Diametre of base of cylinder = diametre of cone = 24 m
$\therefore$ Radius of base = 12 m
Height of cylindedr = 11 m = h${}_1$
Height of Cone = 5 m = h${}_2$
Let slant height of cone be $l$
$l=GD=\sqrt{r^2+h^2}=\sqrt{{12}^2+5^2}=13m$
Area of canvas required = CSA of cylinder + CSA of cone
$=2\pi r{h}_1+\pi rl$
$=\pi r(2h_1+l)$
$=\frac{22}{7}\times 12(2\times 11+13)m^2$
$=\frac{22\times 12}{7}\times 35m^2$
$=22\times 60m^2$
$=1320m^2$
Rate of canvas = Rs. 10 per m${}^2$
$\therefore$ Cost of canvas = Rate $\times$ area of canvas
$=Rs.10\times 1320$
$=Rs.13,200$