Question

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 π=22/7).

Answer 1

The length of canvas used in making the tent is 134.2721 m.

Step-by-step explanation:

Given:

Circumference of the base = 44 m

height conical tent, h = 10 m

width of canvas is 2 m

Now, we know that

Circumference = 2πr

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

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

r = 7 m

We also know that

$l^2=r^2+h^2$

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

$l = \sqrt{49+100$

$l=\sqrt{149} m$

Now,

Curved surface area of canvas = πrl

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

                                                   = $22\sqrt{149}$

So, the length of canvas used in making the tent = $\frac{Area of canvas}{Width of canvas}$      

                                                                                 = $\frac{22\sqrt{149} }{2}$             [given]

                                                                                  = $11\sqrt{149}$

                                                                                  = $11 \times 12.2065$

                                                                                 = 134.2721 m (approx)