a circle has a sector with area 20pi and a central angle of 2/5pi radians. what is the area of the circle?

Answer 1

sector area=20pi=62.832=r^2pi*</360

rad=57.296°

*.4

=22.918°= sec<

r^2pi=62.832/22.918*360

= 2.742 *360

= 986.976sq

Answer 2

First let's convert the radians to degrees. Remember that °π = 180°, so 2π/5 is (2*180)/5 = 72°

A sector is just a fraction of the whole area. Out of 360 degrees we only want 72° so the fraction is 72/360

The area of the circle is π*r²

The area of the sector is

π*r² * (72/360) = 20π

Now let's get rid of the fraction by multiplying both sides by its reciprocal 360/72

π*r² * (72/360) *(360/72)= 20π *(360/72)

π*r2 * = 100π or 314.16

Answer 3

Each complete turn around a circle is 2 pi radians (the same as 360 degrees), so multiplying the ratio of 2 pi / (2/5 pi) will give the area of the circle. Dividing 2 pi by 2/5 pi gives a ratio of 5, so the area of the circle is five times greater than the area of the sector, or 5 x 20 pi = 100 pi.

Hope this helps

Answer 4

This is probably most easily done using a proportion, as follows:

A complete circle consists of a central angle of 2pi. We can equate the fraction of the angle with the fraction of the area:

2/5pi/(2pi)=20pi/Area of circle. The left hand side is 1/5. Taking the reciprocal of both sides,

we get 5 = Area of circle/20pi, so the area of the circle is 100pi.