The circumference of the base of a $10\ m$ height conical tent is $44$ metres. Calculate the length of canvas used in making the tent if width of canvas is $2\ m$. (Use $\pi = \frac{22}{7}$)

 Given:

The circumference of the base of a $10\ m$ height conical tent is $44$ metres. 

The width of canvas is $2\ m$.

To do:

We have to find the length of canvas used in making the tent.

Solution:

Circumference of the base of the conical tent $= 44\ m$
This implies,

Radius of the base $(r)=\frac{44 \times 7}{2 \times 22}$

$=7 \mathrm{~m}$

Height of the tent $(h)=10 \mathrm{~m}$

Slant height of the tent $(l)=\sqrt{r^{2}+h^{2}}$

$=\sqrt{(7)^{2}+(10)^{2}}$

$=\sqrt{49+100}$

$=\sqrt{149} \mathrm{~m}$

Therefore,

Area of the canvas used $=\pi r l$

$=\frac{22}{7} \times 7 \times \sqrt{149}$

$=22 \sqrt{149} \mathrm{~m}^{2}$

Width of the canvas used $=2 \mathrm{~m}$

Length of the canvas used $=\frac{\text { Area }}{\text { Width }}$

$=\frac{22 \sqrt{149}}{2}$

$=11 \sqrt{149}$

$=11 \times 12.206$

$=134.266 \mathrm{~m}$

$=134.27 \mathrm{~m}$

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

49 Views

Kickstart Your Career

Get certified by completing the course

Get Started