Practice Math Questions for Praxis: Area and Circumference of Circles

By Carla Kirkland, Chan Cleveland

When you take the Praxis Core exam, it pays to have a well-rounded knowledge of circles—especially their area and circumference. In the following practice questions, you work both backwards (finding a circle’s radius given its circumference) and forward (finding a circle’s area given its radius).

Practice questions

  1. A circle has a circumference of 20π in.

    What is the radius of the circle?

    A. 4.5 in.
    B. 15 in.
    C. 10 in.
    D. 20 in.
    E. 17.5 in.

    praxis-core-two-circles

  2. The two circles have congruent radii. If the radius of one circle is 3 m, what is the area of the other circle, rounded to the nearest hundredth?

    A.m2
    B. 18 π m2
    C. 14.31 m2
    D. 28.26 m2
    E. 18.35 m2

Answers and explanations

  1. The correct answer is Choice (C).

    The circumference of a circle is 2 times pi times the radius. You can use the formula for circumference, fill in what you know, and solve for r, the radius of the circle:

    PRAXIS_2903

    The radius of the circle is 10 in.

  2. The correct answer is Choice (D).

    The circles’ radii are congruent, which means they have the same measure. Because one circle’s radius is 3 m, the circle in question has a radius of 3 m. You can use the formula for the area of a circle:

    PRAXIS_2904

    Because pi rounded to the nearest hundredth is 3.14, you can multiply 9 by 3.14:

    9 × 3.14 = 28.26

    The area of the circle, rounded to the nearest hundredth, is 28.26 m2.