Question

The diameter of a circle is 20 miles. What is the angle measure of an arc bounding a sector with area 15​ square miles?

Answer 1

diameter = 20 miles
radius = 10 miles
area of entire circle = PI*10*10
area of entire circle = 314.159265 square miles
If a sector is 15 square miles, then the central angle must be (15 / 314.159265) degrees or
17.1887338736 degrees

Answer 2

find area of circle

a=pir^2
d/2=r
20=d
20/2=r=10
a=pi10^2
a=pi100
a=100pi

so 15 squar miles

that is how much of the whole circle

15/100pi
ok, so the angle
360 is full circle

15/100pi=x/360
x is the angle
so usingn math
times both sides by 360
5400/100pi=x
54/pi=x
using calculator
17.1887≈x
about 17 degrees