The area of the sector of the circle is 72п. Find the circumference of this circle if the arc of the sector is 45 degrees.

From the school curriculum in geometry, we well know that in order to determine the area of a sector, you can use this formula:

Sector = πR ^ 2 * a / 360 °.

Let us determine what value will correspond to the radius of our circle, if from the condition we know that the area of its sector is 72π, at an angle of 45 °:

72π = πR ^ 2 * 45 ° / 360 °.

R ^ 2 = 576;

R1 = 24;

R2 = -24 (does not match the condition).

It is now possible to determine what the circumference will be equal to:

2 * 3.14 * 24 = 150.72.

Answer: 150.72.