What is the area of the circle whose circumference is 12pi in terms of pi?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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

=> 36*pi

The required area of the circle is 36*pi

hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

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.

 

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