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 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

Given

Diameter of cylinder $=4m$

Radius of the cone $\left(r\right)=$ Radius of cylinder $=\frac{4}{2}=2m$

Slant height of the cone $\left(l\right)=2.8m$

Height of the cylinder $\left(h\right)=2.1m$

Step 1. Finding the area of the canvas used for making the tent.

Area of canvas $=C.S.A$ of cone$+$ $C.S.A$ of cylinder

$$\begin{gathered} =\mathrm{\pi rl}+2\mathrm{\pi rh} \\ =\mathrm{\pi r}(\mathrm{l}+2\mathrm{h}) \\ =\frac{22}{7}\mathrm{x}2(2.8+2\mathrm{x}2.1) \\ =\frac{44}{7}(2.8+4.2) \\ =\frac{44}{7}\mathrm{x}7 \\ =44{\mathrm{m}}^2 \end{gathered}$$

Step 2. Finding cost of canvas.

Since cost of the canvas of the tent at the rate of $Rs500per{m}^2$.

Therefore ,cost of canvas$=$area of canvas rate $per{m}^2$

$$\begin{gathered} =44x500 \\ =Rs22000 \end{gathered}$$

Hence ,

The area of the cone $=44m^2$

and cost of Canvas $=Rs22000$