Pre-Algebra: Help with the Circumference Formula

Help with Finding the Circumference

The circumference of a circle is the distance around it. Some geometry problems will ask you to find the circumference of a circle by using the circumference formula. It can be written like this:

C = 2 x pi x r

In this formula, 'C' represents the circle's circumference. Pi equals 3.14, and 'r' represents the circle's radius. The radius is the distance from the middle of the circle to its outside edge. To find the circumference, you multiply two by 3.14 by the circle's radius. For instance, if the radius were four meters, you would multiply two by 3.14 by four to get the circumference of 25.12 meters (2 x 3.14 x 4 = 25.12).

Tip: In math equations, pi is often represented by a symbol that looks like a miniature table. Whether it's represented by the symbol or the word 'pi,' it's always equal to 3.14. You may also see the circumference equation written without the multiplication signs, but you still solve it by multiplying the variables together.

Finding Circumference with Diameter

Some geometry problems give you the circle's diameter instead of its radius. The diameter is the length of a line that cuts the circle in half. If you cut a round pie into two equal sections, the line separating them would be the pie's diameter. The diameter (d) is always equal to exactly two times the circle's radius (r), so d = 2r. The equation for finding the circumference when you know the circle's diameter is written like this:

C = d x pi

To work out the circumference using this formula, just multiply the circle's diameter by 3.14. For instance, if the diameter is seven inches, multiply that by 3.14 to get the circumference of 21.98 (7 x 3.14 = 21.98).

Tip: The commutative property of multiplication tells us that you can multiply values in any order and the answer will be the same. You could write 'C = pi x d' and your answer would not change.

Practice Problems

Here are a few problems to help you practice using these formulas. For some, you'll use the formula C = d x pi, and for others, you'll use C = 2 x pi x r.

1. Every day, Eleanor goes jogging around the circular pond at her local park. She knows that the pond is 0.5 kilometers in diameter. How far does Eleanor jog if she goes around the pond once?

Use the formula C = d x pi to solve this problem, since you know the pond's diameter. Multiply 0.5 km by 3.14 to get the solution, 1.57 km (0.5 x 3.14 = 1.57).

2. Jamal has his friends over for a birthday party, and his Mom orders them a pizza. The circular pizza is cut into slices, and the edge of each slice measured from the center of the pizza to the outside of the crust is 11 centimeters long. What is the pizza's circumference?

To find the circumference, you can use the formula C = 2 x pi x r, since you know the pizza's radius is 11 cm. You multiply two times 3.14 times 11 cm to get the solution, 69.08 cm (2 x 3.14 x 11 = 69.08).

3. Challenge Question: A scientist measures a tree trunk's circumference and finds that it is equal to eight feet. What is the diameter of the tree trunk, and what is its radius?

Hint: Remember that the radius is equal to half of the diameter.

There are several different ways to solve this problem. Since you know that circumference is equal to the circle's diameter times 3.14, you could divide the circumference, eight feet, by 3.14. This would give you the diameter, which is approximately 2.55 feet (8 ÷ 3.14 = 2.55). Now that you know the diameter, you can divide it by two to get the tree's radius of approximately 1.27 feet (2.55 ÷ 2 = 1.27).

You could also find the radius first by dividing the circumference by two and 3.14 (8 ÷ 2 ÷ 3.14 = 1.27). Then, to find the diameter, you would multiply the radius by two (1.27 x 2 = 2.55).