Question

Find the measure of in degrees, given that the shaded region has an area of 45.27 square centimeters. If necessary, round your answer to two decimal places..

Answer 1

Find the measure of arc DF**

Answer 2

You get the angle from this:

Angle / 360 degrees = 45,27 cm^2 / pii * r^2

Proportion of angles is equal to proportion of areas

Then arc DF : angle/ 360 degrees = length DF/ 2* pii * r,

Answer 3

measure of arc DF in degrees is the angle arc DF makes at the center of the circle.
The whole circle has an area of (pi)r^2 and it makes 360 degrees at the center.
Therefore, area 45.27 will make: 45.27 * 360 / { (pi)r^2 } = 45.27 * 360 / { (pi) 6^2 }

Answer 4

Thankyou guys (: @Gebooors @ranga

Answer 5

You are welcome!