An arc of length 20π cm subtends an angle of 144° at the centre of a

1.	An arc of length 20π cm subtends an angle of 144° at the centre of a circle. Find the radius of the circle.
Answer» Given, Length of arc = 20π cm And. θ = Angle subtended at the centre of circle = 144° We know that, Length of arc = θ/360 ∗ 2πr cm θ/360 ∗ 2πr cm = 144/360 ∗ 2πr cm = 4π/5 ∗ r cm From the question, we can equate 20π cm = 4π/5 ∗ r cm r = 25 cm. Thus, the radius of the circle is 25 cm.

An arc of length 20π cm subtends an angle of 144° at the centre of a circle. Find the radius of the circle.

Answer»

Given,

Length of arc = 20π cm

And. θ = Angle subtended at the centre of circle = 144°

We know that,

Length of arc = θ/360 ∗ 2πr cm

θ/360 ∗ 2πr cm = 144/360 ∗ 2πr cm = 4π/5 ∗ r cm

From the question, we can equate

20π cm = 4π/5 ∗ r cm

r = 25 cm.

Thus, the radius of the circle is 25 cm.