Hi, there--

The Problem:
The Circumference of a circle is 24pi feet. Find both the area and the diameter of the circle?

Solution:
The formula for the circumference of a circle is 
C = 2*pi*r

Since the circumference of the circle is 24pi feet, we have
24*pi = 2*pi*r

Simplify and solve for r
2r = 24 
r = 12

The radius of the circle is 12 feet.

The formula for the Area of a circle is pi*r^2. Since the radius is 12, we have
A = pi*(12)^2

Simplify.
A = pi*144
A=144pi

The area of the circle is 144pi square feet.

The diameter is twice the radius, so the diameter is 12*2=24 feet.

That's it. Please email me if you have questions or comments about the solution. 
I appreciate your feedback.

Ms.Figgy
math.in.the.vortex@gmail.com