Question

The circumference of the base of a $10m$ high conical tent is $44$ metres. Then the length of canvas used in making the tent, if width of canvas is $2m$ is (Use $\pi =22/7$) :

• A. $132.2m$
• B. $134.2m$
• C. $130.2m$
• D. $136.2m$

Answer 1

The correct option is B $134.2m$

Let $r$ $m$ be the radius of the base, $h$ $m$ be the height and $l$ $m$ be the slant height of the cone.

Given, circumference $=44$ metres.

$\Rightarrow 2\pi r=44\Rightarrow 2\times \frac{22}{7}\times r=44\Rightarrow r=7$ metres.

It is also given that $h=10$ metres.

$\therefore$ Slant height $l^2=r^2+h^2\Rightarrow l=\sqrt{r^2+h^2}$

$=\sqrt{49+100}=\sqrt{149}=12.2m$.

Now, we know, the surface area of the tent $=\pi rl$.

$=\frac{22}{7}\times 7\times 12.2m^2=268.4m^2$

$\therefore$ Area of the canvas used $=268.4m^2$.

It is given that the width of the canvas is $2$ $m$.

$\therefore$ Length of the canvas used $=\frac{\text{area}}{\text{width}}=\frac{268.4}{2}=134.2m$.

Hence, option $B$ is correct.