Question

A sector of a circle has an area of 32πcm^2and contains a central angle of 210 degrees.calculate the radius of a circle

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the radius of the circle, we first need to determine the radius of the sector using the given area and central angle.

The formula for the area of a sector of a circle is:

Area = (θ/360) * π * r^2,

where θ is the central angle in degrees and r is the radius of the circle.

Given that the area of the sector is 32π cm^2 and the central angle is 210 degrees, we can plug in these values into the formula:

32π = (210/360) * π * r^2
32 = (7/12) * r^2
r^2 = (12/7) * 32
r^2 = 12 * 4.57
r^2 = 54.84
r = √54.84
r ≈ 7.4 cm

Therefore, the radius of the circle is approximately 7.4 cm.