The circumference of the base of a 10 m height conical tent is 44m,

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

 

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