Question

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

Answer 1

A=(απr^2)/360=(απd^2)/1440 (r^2=d^2/4)

α=1440A/(πd^2)

s=απd/360 (where s=arc length) so

s=(1440Aπd)/(360πd^2)

s=4A/d and since A=10mi^2 and d=20mi

s=(4*10)/20

s=2 miles