If a circular pool has a circular fence around it that has a 20-foot diameter, then what is the measure of the central angle that cuts the arc that measures 4 feet?

Answer 1

To find the measure of the central angle that cuts the arc measuring 4 feet, we first need to find the total circumference of the circular fence.

Given that the diameter of the circular fence is 20 feet, the radius would be half of that, which is 10 feet.

The circumference of a circle is given by the formula:
circumference = 2 * π * radius

Substitute the values:
circumference = 2 * π * 10
circumference = 20π feet

Now, we need to find the central angle that cuts the arc measuring 4 feet.

The formula to find the measure of the central angle is:
angle = (arc length / circumference) * 360°

Substitute the values:
angle = (4 / 20π) * 360
angle = (0.2π) * 360
angle = 72°

Therefore, the measure of the central angle that cuts the arc measuring 4 feet is 72°.