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

Solution:  Let $r$ m be the radius of the base , $h$ m be the height and $l$ m be the slant height of the cone . then,

Circumference = 44 metres

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

It is given that $h=10 metre$

$\therefore$                            $l^2=r^2+h^2\Rightarrow l=\sqrt{r^2+h^2}=\sqrt{49+100}=12.2m$

Surface area of the tent    $=\pi rl=\frac{22}{7}\times 7\times 12.2=268.4m^2$

$\therefore$          Area of the canvas used $=268.4 m^2$

It is given that the width of the canvas is 2 m .

$\therefore$                    Length of the canvas used    $=\frac{Area}{width}=\frac{268.4}{2}=134.2m$

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