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.)

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Given:

A tent is in the shape of a cylinder surmounted by a conical top.

The height and diameter of cylindrical part are $2.1\ m$ and $4\ m$ respectively and the slant height of the top is $2.8\ m$.

To do:

We have to find the cost of canvas needed to make the tent if the canvas is available at the rate of Rs. 500/sq. meter.

Solution:

For conical portion, we have

$r=2\ m$ and $l=2.8\ m$

$\therefore \ S_{1}=$Curved surface area of conical portion

$\therefore \ S_{1} \ =\ \pi rl$

$=\pi \times \ 2\ \times \ 2.8$

$=\ 5.6\pi \ m^{2}$

For cylindrical portion, we have

$r =2\ m$ and $h= 2.1\ m$

$\therefore \ S_{2} =$Curved surface area of cylindrical portion

$\therefore \ S_{2} \ =\ 2\pi rh$

$=2 \times \pi \ \times \ 2\ \times \ 2.1$

$=8.4\pi \ m^{2}$

Area of canvas used for making the tent $S_{1}+S_{2}=5.6\pi+8.4\pi$

$=14\pi\ cm^{2}$

$=14\times \frac{22}{7}$

$=44\ m^{2}$

Total cost of the canvas at the rate of Rs.500 per $m^{2}=Rs.( 500\times44)$

$=Rs.\ 22000$

Updated on 10-Oct-2022 13:24:34