Question

In a circle with a diameter of 32, the area of a sector is 512π 3 . the measure of the angle of the sector, in radians, is

Answer 1

The measure of the angle of the sector in a circle with a diameter of 32 and the area of the sector being 512π/3 is 4π/3 radians.

Step-by-step explanation:

To find the measure of the angle of the sector in radians, given the area of the sector (512π/3) and the diameter of the circle (32), we use the formula for the area of a sector which is A = (1/2) * r² * Θ where A is the area, r is the radius, and Θ is the central angle in radians.

First, we find the radius (r) by dividing the diameter by 2: r = diameter / 2 = 32 / 2 = 16.

Next, we can rearrange the formula to solve for Θ: Θ = (2 * A) / r². Plugging in the values, we get Θ = (2 * 512π/3) / 16².

Performing the calculations gives us Θ = (2 * 512π/3) / (16 * 16) = 1024π/3 / 256 = 4π/3 radians.

Therefore, the measure of the angle of the sector is 4π/3 radians.

Answer 2

4π/3 hope this helps