Question

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

• A. 12,500
• B. 14,500
• C. 16,500
• D. 18,500

Answer 1

The correct option is C 16,500

Given,
Height of the cylinder, $h=2.1m$
Diameter of the cylinder, $d=3m$
Slant height of conical part, $l=2.8m$

Area of canvas required
= Curved surface area of cylinder + Curved surface area of cone
$=2\pi rh+\pi rl$
$=2\times \frac{22}{7}\times \frac{3}{2}\times 2.1+\frac{22}{7}\times \frac{3}{2}\times 2.8$
$=\frac{22}{7}(6.3+4.2)$
$=\frac{22}{7}\times 10.5$
$=33m^2$

So, cost of canvas at the rate of $₹500/m^2$ is
$=33\times 500$
$=₹16,500$