an arc of a circle is of length 5 pi cm and sector it bounds has an area of 20 - Maths - Areas Related to Circles

Question

an arc of a circle is of length 5 pi cm and sector it bounds has
an area of 20 pi cm2 find the radius of the circle

Priyanka Kedia · Accepted Answer

Let the radius of the circle = r cm

Given, length of an arc of the circle = 5 $π$ cm

and, area of sector = $20 π {c m}^{2}$

we know that, length of an arc of the circle $= \frac{θ (2 π r)}{360^{0}}$

Therefore,

$\frac{θ (2 π r)}{360^{0}} = 5 π \Rightarrow θ r = 900 \Rightarrow θ = \frac{900}{r} ...... (1)$

And,

$A r e a o f \sec t o r = \frac{π r^{2} θ}{360^{0}}$

Therefore,

$\frac{π r^{2} θ}{360^{0}} = 20 π \Rightarrow r^{2} θ = 7200 ....... (2)$

Substitute Value of $θ$ from equation (1) in equation (2), we get,

$r^{2} (\frac{900}{r}) = 7200 \Rightarrow r = \frac{7200}{900} \Rightarrow r = 8 c m$

Hence, radius of the circle is 8 cm.

an arc of a circle is of length 5 pi cm and sector it bounds has an area of 20 pi cm2. find the radius of the circle.