Mathematics Knowledge  Circumference Answer

In working as an ASVAB tutor, I decided to write a book entitled, The ASVAB Tutor’s Mathematics Knowledge Study Guide.  In my book and in my course, I review 15 subtopics in Mathematics Knowledge.  Most of these topics are related to algebra and geometry.

Yesterday I presented a Mathematics Knowledge question about geometry.

The question is about a circle.

The question is:

If the circumference of a circle is 10 pi, what is the area?

  1. 5 pi
  2. 10 pi
  3. 25 pi
  4. 100 pi

In order to solve this problem, it is necessary to know the formula for the circumference of a circle and the area of a circle.

The circumference of a circle is pi x d = 3.14 x diameter

The area of a circle is pi x r2 = 3.132 x radius squared.

The circumference is 10p.

Since the formula for circumference is pd, then in this example d = 10.

When the diameter is 10, the radius is 5 since the radius is ½ of the diameter.

To find the area, I plug 5 in for radius into the area formula.

A = pi x r2

A =  pi x 52 = 25pi

The area of the circle is choice C. 25pi