Hard Geometry Question?

Formula:

Area of the sector ( x degrees , radius r ) = (x/360) pi r^2

The angle subtended by the sector, divided by the full-circle angle (360 if degrees, 2*pi if radians, etc.) is the fraction of the full circle area that the sector occupies. Your sector is 72/360 = 1/5 of a full circle. You are told that this is 5*pi. You also know that the full circle area is pi*r^2, where r is the radius of the circle. Put that together in an equation and you get:

(sector area) = (1/5)*(circle area)

5*pi = (1/5)(pi*r^2)

...and solve this for r. Multiply both sides by 5/pi:

25 = r^2

r = 5

Algebraically, r=-5 is also a solution, but a circle can't have a negative radius, so that's not a "real" solution. The radius is 5.

A sector whose central angle is 72 degrees has an area which is 1/5th (72/360) of the total area of the circle.

The whole area is 5 x 5pi= 25pi

Area = pi x radius squared

radius squared = ?

Over to you.

Area=pi*r²

5pi*360/72=pi*r² (5*360/72 because 5 is 1/72 of the full area, so 360*72/72 just leaves us with 360 degrees)

r=sqrt(25)

=5

Edit: Misread question.

If you know the area, you don't need the central angle to figure out the radius. Just use this equation

5pi=pi*r^2

divide each side by pi

5=r^2

r=sqrt(5)

which is about

2.2361