Question

A tent is in the shape of a cylinder surmounted by a conical top of same diameter. If the height and diameter of cylindrical part are 2.1 m and 3 m respectively and the slant height of conical part is 2.8 m, then find the cost of canvas needed to make the tent if the canvas is available at the rate of ₹500 per sq. metres. [Use $\pi =\frac{22}{7}$]

Answer 1

• Given dimensions of cylinder potion:

Diameter of cylinder = 3 m
Radius of cylinder = 3/2 = 1.5 m
Height of cylinder = 2.1 m

• Given dimensions of conical portion:

Radius of the conical part = radius of cylindrical part
Radius of the conical part = 1.5 m
Slant height of conical top = 2.8 m

• Canvas needed to make the tent = Curved surface area of the conical portion + curved surface area of the cylindrical portion

Curved surface area of cylindrical portion
$=2\pi rh$
$=2\times \left(\frac{22}{7}\right)\times 1.5\times 2.1$
$=19.8sq.m.$

Curved surface area of conical portion
$=\pi rl$
$=\left(\frac{22}{7}\right)\times 1.5\times 2.8$
$=13.2sq.m.$

Total curved surface area
$=19.8+13.2$
$=33sq.m.$

• Canvas needed to make the tent $=33sq.m.$

Cost of 1 sq.m. canvas = Rs. 500
Cost of 33 sq.m. canvas = 33×500 = Rs. 16,500

• Therefore, it will cost Rs. 16,500 for making such a tent.