Question

Find the area of the sector of a circle of radius 10cm if the length of the arc bounding the sector is 30cm?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the area of the sector, we first need to find the angle at the center of the circle that corresponds to the given arc length.

We know that the total circumference of the circle is 2πr = 2π(10) = 20π cm.

Since the arc length is 30 cm, it corresponds to an angle at the center of the circle, given by:

θ = (arc length / circumference) * 360 = (30 / 20π) * 360 ≈ 54.55 degrees

Now, we can find the area of the sector using the formula:

Area of sector = (θ/360) * πr^2 = (54.55/360) * π(10)^2 ≈ 15.91 cm^2

Therefore, the area of the sector of a circle of radius 10 cm with an arc length of 30 cm is approximately 15.91 cm^2.