SOLUTION: How do you calculate the shaded area inside the circle of perimeter 50 pi units?

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Question 420197: How do you calculate the shaded area inside the circle of perimeter 50 pi units?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the formula for the circumference of a circle is equal to 2 * pi * r

pi is a constant that is equal to 3.141592654

r is the radius of the circle.

the circumference of the circle is the same as the perimeter of the circle.

use the equation to solve for r.

you get:

2 * pi * r = 50

divide both sides of the equation by 2 * pi to get:

r = 50 / (2 * pi)

this can be simplified to r = 50 / 6.283185307 which can further simplified to:

r = 7.957747155

the formula for the area of a circle is equal to pi * r^2.

that would be the shaded area inside the circle.

use the value you just got for r to find the area.

your formula is:

pi * r^2 = area of the circle.

r = 7.957747155 so we substitute in the equation for r to get:

pi * (7.957747155)^2 = area of the circle.

this can be simplified to be:

3.141592654 * 63.32573978 = 198.9436789 square units.

the perimeter is 50 units.
the radius is 7.957747155 units.
the area is 198.9436789 square units.