The circumference of a circle = 20 pi. If the circle is cut in half, what is the area of one of the resultant halves ?
please answer and explain
C = 2 r pi
20 pi = 2 r pi Divide both sides by 2 pi
10 = r
r = 10
A = r ^ 2 pi
A = 10 ^ 2 pi
A = 100 pi
A / 2 = 100 / 2 = 50 pi
To find the area of one of the resultant halves when a circle is cut in half, we first need to find the radius of the original circle.
The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius. In this case, we have the circumference as 20π. Therefore, we can set up the equation as follows:
20π = 2πr
To find the radius, we can divide both sides of the equation by 2π:
r = 20π / (2π)
r = 10
Now that we have the radius, we can find the area of one of the resultant halves. The formula for the area of a circle is A = πr^2, where A is the area and r is the radius. Plugging in the radius we found (r = 10) into the formula, we get:
A = π(10)^2
A = π(100)
A = 100π
Therefore, the area of one of the resultant halves is 100π.