Find R of the circle if the sector area is 20pi cm2 and the center of the angle is 75 °.

A circle is a part of a plane bounded by a circle.

A circular sector is the part of a circle between two radii.

In order to find the length of the radius of a given circle, we use the formula for the area of a circular sector:

S = πr ^ 2α / 360º, where:

S is the area of the circular sector;

r is the radius of the circle;

α is the central angle;

π – 3.14;

πr ^ 2α = S · 360º;

r ^ 2 = (S * 360º) / (π * α);

r ^ 2 = (20π * 360º) / (π * 75º) = 7200π / 75π = 96;

r = √96 ≈ 9.8 cm.

Answer: The radius of the circle is 9.8 cm.