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 m². (Note that the base of the tent will not be covered with canvas.) [Use \(\pi =\frac{22 }{7}\)]

Answer 1

The height (h) of the cylindrical part = 2.1 m 
The diameter of the cylindrical part = 4 m 
The radius of the cylindrical part = 2 m 
Slant height \((l)\)of conical part = 2.8 m 
The required surface area of the tent = surface area of the cone + surface area of the cylinder
\(= \pi rl+2\pi rh\)
\(= \pi r(l+2h)\)
\(= (\frac{22}{7})×2\times(2.8+2×2.1)\)

\(= (\frac{44}{7})(2.8+4.2)\)

\(= (\frac{44}{7})×7 = 44 \ \ m^2\)

Cost of 1 m² canvas = Rs 500
Cost of 44 m² canvas = 44 × 500 = 22000 
Therefore, it will cost Rs 22000 to make such a tent.