the area of sector AOB is 36pi and measure of the angle AOB is 40. Find the radius of circle O.?

Answer 1

You can use the standard area formula for a circle for this problem. All you need to do is find out what fraction of the circle the sector is. Its angle is 40°, and as you know, a whole circle is 360°.

40°/360° = 1/9

So you know to reduce the area formula by 1/9.

(πr^2)/9

Set it equal to the area you're given.

36π=(πr^2)/9

And then just solve for r

Multiply by 9 on each side

324π=πr^2

Cancel out the π's

324=r^2

Take the square root of both sides

18=r

And there's your answer!

Answer 2

pi r^2 40 / 360 =36 pi

r=18