Question:
The circumference of the base of a 10 m height conical tent is 44m, calculate the length of canvas used in making the tent if width of canvas is 2 m.
Solution:
We know that
C.S.A of cone = πrl
Given circumference = 2πr
⟹ 2 ∗ 227 ∗ r = 44
⟹ r/7 = 1
⟹ r = 7 m
Therefore
$\mathrm{l}=\sqrt{\mathrm{r}^{2}+\mathrm{h}^{2}}$
$=\sqrt{7^{2}+10^{2}}$
$\mathrm{l}=\sqrt{149} \mathrm{~m}$
Therefore C.S.A of tent = πrl
$=\frac{22}{7} * 7 * \sqrt{149}$
$=22 \sqrt{149}$
Therefore the length of canvas used in making the tent
$=\frac{\text { Area of canvas }}{\text { Width of canvas }}$
$=\frac{22}{2 \sqrt{149}}$
$=\frac{11}{\sqrt{149}}$
= 134.2 m