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 $2.1\text{m}$ and $4\text{m}$, and slant height of the top is $2.8\text{m}$, find the area of the canvas used for making the tent. Also, find the cost of canvas of the tent at the rate of $\text{Rs.}500/{\text{m}}^2$

Answer 1

Lets form a conical tent according to according to given information,

For conical portion we have

$r=2\text{m};l=2.8\text{m}$

$S_1=$ curved surface area of conical portion

$\Rightarrow S_1=\pi rl$

$\Rightarrow S_1=\pi \times 2\times 2.8m^2$

$\Rightarrow S_1=5.6\pi {\text{m}}^2$

for the cylindrical portion, we have

$r=2\text{m};l=2.1\text{m}$

$S_2=$ curved surface area of the cylindrical portion

$\Rightarrow S_2=2\pi rh=2\pi \times 2\text{m}\times 2.1\text{m}=8.4\pi m^2$

Area of the canvas used for makine the tent,

$=S_1+S_2=(5.6\pi +8.4\pi )m^2=14\times \frac{22}{7}{m}^2=44m^2$

It is given that, the rate of the canvas is $\text{Rs.}500/{\text{m}}^2$
$\Rightarrow$ Total cost of the canvas at the rate of $\text{Rs.}500/{\text{m}}^2=\text{Rs.}(500\times 44)=\text{Rs.}22000$