Question

The circumference of the base of a $10m$ high conical tent is $44m$. Calculate the length of the canvas used in making the tent if the width of the canvas is $2m$.

• A. $137.5m$
• B. $134.2m$
• C. $130m$
• D. $119m$

Answer 1

Answer: (B)

$134.2m$

Let $r$ be the radius of the base of the conical tent.

Now,

$2\pi r=44$

$2\times \frac{22}{7}\times r=44$

$r=\frac{44\times 7}{22\times 2}$

$r=7m$.

Curved surface area of the tent $=\pi rL$

$L=\sqrt{7^2+{10}^2}$

$L=\sqrt{49+100}$

$L=\sqrt{149}$

CSA $=\pi rl=\frac{22}{7}\times 7\times \sqrt{149}$

$=22\sqrt{149}{m}^2$.

Now,

$22\sqrt{149}=2\times l$

$l=11\sqrt{149}$

$l=134.2m$.

Hence, the required length of the canvas is $134.2m$.