What is the area of the circle whose circumference is 12pi in terms of pi?
Given the circumference of the circle is 12pi.
We need to find the area of the circle.
We know that the area of a circle is given by:
A = r^2 * pi such that r is the radius.
Also, we know that the circumference is given by:
C = 2*r * pi
But C = 12*pi
==> 2*r*pi = 12*pi
We will divide by 2pi.
==> r = 12pi/2pi = 6.
Then the radius is r= 6, we will substitute into A.
==> A = r^2 * pi = 6^2 * pi = 36pi.
Then the area of the circle in terms of pi is : A = 36pi square units.
The area of a circle with a radius r is given by pi*r^2 and the circumference of a circle with radius r is 2*pi*r.
Here we have a circle with a circumference 12*pi
2*pi*r = 12*pi
=> r = 6
Area = pi*6^2
The required area of the circle is 36*pi