Question

A tent of height $77dm$ is in the form of a right circular cylinder of diameter $36m$ and height $44dm$ surmounted by a right circular cone. Find the cost of the canvas at $Rs.3.50$ per square meter.

Answer 1

The radius of cylinder and radius of cone both will be equal to $18m.$

As we know that,

$1m=10dm$

So, $1dm=0.1m$

Therefore,

Height of the tent $=77dm$

$=77\times 0.1m$

$=7.7m$

Height of cylinder $=44dm$

$=44\times 0.1m$

$=4.4m$

Height of cone $=7.7-4.4$

$=3.3m$

The slant height of the cone can be calculated by using height and the radius of the cone,

$\begin{array}{cc}l& =\sqrt{R^2+H^2}\\ & =\sqrt{{\left(18\right)}^2+{\left(3.3\right)}^2}\\ & =\sqrt{324+10.89}\\ & =\sqrt{334.89}\\ & =18.3m\end{array}$

Total surface area of tent $=\pi Rl+2\pi R{H}_{cylinder}$

$=\pi R(l+2H_{cylinder})$

$=\pi \times 18(18.3+2\times 4.4)$

$=18\pi \times 27.1$

$=1532.46m^2$

The total cost of canvas $=$ Cost of canvas per square meter $\times$ Surface area of the tent in square meters

$=1532.46\times 3.5$

$=Rs.5363.64$