if a circle has an area 2500 times pi what is the circumference? Please show work.
A = pi * r^2
The square root of 2500 = 50
The diameter must be 100
C = pi * d
1250
To find the circumference of a circle, you can use the formula:
C = 2πr
Where C represents the circumference and r is the radius of the circle.
In this case, we are given that the area of the circle is 2500 times π. The formula for the area of a circle is:
A = πr^2
We can set up an equation using these two formulas:
2500π = πr^2
To solve for r, we divide both sides of the equation by π:
2500 = r^2
Taking the square root of both sides, we find:
r = √2500
Simplifying the square root:
r = 50
Now that we know the radius is 50, we can substitute it into the circumference formula:
C = 2π(50)
Simplifying further:
C = 100π
Therefore, the circumference of the circle is 100π units.