An arc of a circle is of length 5π cm and the sector it bounds has an area of 20 π cm2. Find the radius of the circle. - Mathematics

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Sum

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

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Solution

Let the radius of the circle be r cm and the arc AB of length 5π cm subtends angle θ at the centre O of the circle. Then,

Arc AB = 5π cm and

Area of sector OAB = 20π cm2

`\Rightarrow \frac{\theta }{360}\times 2\pi r=5\pi \text{ and}\frac{\theta }{360}\times \pi r^{2}=20\pi`

`\Rightarrow \frac{\frac{\theta }{360}\times \pi r^{2}}{\frac{\theta}{360}\times 2\pi r}=\frac{20\pi }{5\pi }`

⇒ r/2 = 4 ⇒ r = 8 cm

ALTER: We have, Area = 1/2 /l /r ⇒20π

= 1/2 × 5π × r = 8 cm

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