An arc of a circle subtends an angle 36° at a point on its circumference. What is the area (in cm2 ) of the sector if the arc of its length is 3∗𝜋5 𝑐𝑚?

To solve this problem, we need to use the formula for the area of a sector of a circle, which is given by:

Area of sector = (θ/360) * π * r²

Where: θ is the angle the sector subtends at the centre of the circle (in degrees), r is the radius of the circle.

However, we don't know the radius of the circle. But we do know the length of the arc, which is given by:

Arc length = θ/360 * 2πr

We can rearrange this formula to find r:

r = Arc length / (θ/360 * 2π)

Substituting the given values:

r = 3π/5 / (36/360 * 2π) r = 3π/5 / (π/5) r = 3 cm

Now we can substitute r = 3 cm into the formula for the area of a sector:

Area of sector = (36/360) * π * 3² Area of sector = (1/10) * π * 9 Area of sector = 9/10 π cm²

So, the area of the sector is 9/10 π cm².