Question

The radius of a circle is 20 miles. What is the angle measure of an arc bounding a sector with area 10π square miles?

Answer 1

Area of a sector = n/360 (pi)(radius)^2

Answer 2

Knowing the radius find the area of the circle.

A full circle is 360 degrees.

So 360 degrees is equivalent to full area of the circle
x degree is equivalent to 10(pi)

It is a proportion problem. Solve for x.

Answer 3

So 360-10(pi)?

Answer 4

360 / ((pi)(r^2)) = x/(10pi)

Answer 5

Is the answer \[\approx 1\]

Answer 6

Not 1 i meant 11.4

Answer 7

mopsy...?

Answer 8

x / 10pi = 360 /((pi)(r^2))

To isolate x, multiply both sides by 10pi

x = 360 /((pi)(r^2)) (10pi) = 3600/r^2 = 3600 / 20^2 = 9 degrees