# 7.    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 m2. (Note that the base of the tent will not be covered with canvas.)

D Devendra Khairwa

The canvas will cover the cylindrical part as well as the conical part.

So,     the area of canvas   =   Area of cylindrical part (curved)   +   Area of the conical part

Now, the area of the cylindrical part is  $=\ 2\pi rh$

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

or                                                       $=\ 8.4 \pi\ m^2$

And the area of the cone is   $=\ \pi rl$

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

or                                       $=\ 5.6\pi\ m^2$

Thus, the area of the canvas     $=\ 8.4\pi\ +\ 5.6\pi$

or                                            $=\ 14\pi\ =\ 44\ m^2$

Further, it is given that the rate of canvas per m2  is  =  Rs. 500.

Thus the required money is   $=\ 500\times 44\ =\ Rs.\ 22,000$

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