Question

The area of the sector of a circle bounded by an arc of length 4cm is equal to 20 cm2. find the radius of the circle.

Answer 1

[ Figure in the attachment ]

Given :- Length of Arc = 4 cm

area of sector = 20 cm²

Solution :-

Let radius be r cm
and
$theta \: denoted \: by \: \alpha$

$length \: of \: arc = \frac{ \alpha }{360} \times 2\pi \: r$


$4 = \frac{ \alpha }{180} \times \pi \: r$

$720 = \alpha \pi \: r \: .........(i)$


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$area \: of \: sector = \frac{ \alpha }{360} \times \pi \: {r}^{2}$


$20 = \frac{ \alpha }{360} \pi \: r \: \times \: r$


$7200 = (\alpha \: \pi \: r \: )r \: .........(ii)$


Put the value of ( i ) in Second :-


$7200 = ( \alpha \pi \: r)r$


$7200 = 720 \times r$


$\frac{7200 }{720} = r$

10 = r

Radius of circle = 10 cm