Learn on PengiReveal Math, AcceleratedUnit 12: Area, Surface Area, and Volume

Lesson 12-4: Solve Problems Involving Circumference of Circles

In this Grade 7 lesson from Reveal Math, Accelerated (Unit 12), students learn how to solve problems involving the circumference of circles by exploring the constant ratio of circumference to diameter known as pi (π ≈ 3.14) and applying the formulas C = πd and C = 2πr. Using real-world contexts like circular horse training pens and Ferris wheels, students practice calculating circumference given either the radius or diameter. The lesson builds conceptual understanding of the relationships between radius, diameter, and circumference before applying those skills to multi-step problems.

Section 1

Circumference of a Circle

Property

The distance from the center of a circle to any point on the circle itself is called the radius of the circle.
The diameter of a circle is the length of a line segment joining two points on the circle and passing through the center. Thus, the diameter of a circle is twice its radius.
The perimeter of a circle is called its circumference.
The circumference $C$ of a circle is given by

C = \pi \times d

where $d$ is the diameter of the circle. The Greek letter $\pi$ (pi) stands for an irrational number: $\pi = 3.141592654 ...$

Examples

A circular pool has a diameter of 10 meters. Its circumference is $C = \pi \times 10 \approx 31.42$ meters.
A bicycle wheel has a radius of 14 inches. Its diameter is $2 \times 14 = 28$ inches, so its circumference is $C = \pi \times 28 \approx 87.96$ inches.
If a running track has a circumference of 400 meters, its diameter can be found by $d = \frac{C}{\pi} = \frac{400}{\pi} \approx 127.32$ meters.

Explanation

Circumference is the special name for a circle's perimeter. It's the distance around the circle's edge. This distance is always a little more than 3 times the circle's diameter, a constant ratio we call pi ( $\pi$ ).

Section 2

Pi and the Circumference Formulas

Property

The perimeter (distance around the outside) of a circle has a special name: Circumference (C).

For every circle in the universe, if you divide its circumference by its diameter, you always get the same magical number: $\pi$ (Pi).

$\pi$ is an irrational number that goes on forever (3.14159...), but we usually approximate it as 3.14 or $\frac{22}{7}$ .
Formulas for Circumference:

C = \pi d

C = 2\pi r

Examples

A circular pool has a diameter of 10 meters. Using 3.14 for $\pi$ , its circumference is roughly 3.14 x 10 = 31.4 meters.
A bicycle wheel has a radius of 14 inches. Using $\frac{22}{7}$ for $\pi$ , its circumference is:

C = 2 \times \frac{22}{7} \times 14 = 88 \text{ inches}

Section 3

Finding Diameter from Circumference

Property

To estimate the diameter when given the circumference, use the rearranged circumference formula:

d = \frac{C}{\pi}

Since $\pi \approx 3.14$ , you can estimate: $d \approx \frac{C}{3.14}$

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Circumference of a Circle

Property

C = \pi \times d

where $d$ is the diameter of the circle. The Greek letter $\pi$ (pi) stands for an irrational number: $\pi = 3.141592654 ...$

Examples

A circular pool has a diameter of 10 meters. Its circumference is $C = \pi \times 10 \approx 31.42$ meters.
A bicycle wheel has a radius of 14 inches. Its diameter is $2 \times 14 = 28$ inches, so its circumference is $C = \pi \times 28 \approx 87.96$ inches.
If a running track has a circumference of 400 meters, its diameter can be found by $d = \frac{C}{\pi} = \frac{400}{\pi} \approx 127.32$ meters.

Explanation

Section 2

Pi and the Circumference Formulas

Property

The perimeter (distance around the outside) of a circle has a special name: Circumference (C).

For every circle in the universe, if you divide its circumference by its diameter, you always get the same magical number: $\pi$ (Pi).

$\pi$ is an irrational number that goes on forever (3.14159...), but we usually approximate it as 3.14 or $\frac{22}{7}$ .
Formulas for Circumference:

C = \pi d

C = 2\pi r

Examples

A circular pool has a diameter of 10 meters. Using 3.14 for $\pi$ , its circumference is roughly 3.14 x 10 = 31.4 meters.
A bicycle wheel has a radius of 14 inches. Using $\frac{22}{7}$ for $\pi$ , its circumference is:

C = 2 \times \frac{22}{7} \times 14 = 88 \text{ inches}

Section 3

Finding Diameter from Circumference

Property

To estimate the diameter when given the circumference, use the rearranged circumference formula:

d = \frac{C}{\pi}

Since $\pi \approx 3.14$ , you can estimate: $d \approx \frac{C}{3.14}$

Overview

Lesson overview

Review the lesson summary and core properties without leaving the current page.

Overview

Section 1

Circumference of a Circle

Property

C = \pi \times d

where $d$ is the diameter of the circle. The Greek letter $\pi$ (pi) stands for an irrational number: $\pi = 3.141592654 ...$

Examples

A circular pool has a diameter of 10 meters. Its circumference is $C = \pi \times 10 \approx 31.42$ meters.
A bicycle wheel has a radius of 14 inches. Its diameter is $2 \times 14 = 28$ inches, so its circumference is $C = \pi \times 28 \approx 87.96$ inches.
If a running track has a circumference of 400 meters, its diameter can be found by $d = \frac{C}{\pi} = \frac{400}{\pi} \approx 127.32$ meters.

Explanation

Section 2

Pi and the Circumference Formulas

Property

The perimeter (distance around the outside) of a circle has a special name: Circumference (C).

For every circle in the universe, if you divide its circumference by its diameter, you always get the same magical number: $\pi$ (Pi).

$\pi$ is an irrational number that goes on forever (3.14159...), but we usually approximate it as 3.14 or $\frac{22}{7}$ .
Formulas for Circumference:

C = \pi d

C = 2\pi r

Examples

A circular pool has a diameter of 10 meters. Using 3.14 for $\pi$ , its circumference is roughly 3.14 x 10 = 31.4 meters.
A bicycle wheel has a radius of 14 inches. Using $\frac{22}{7}$ for $\pi$ , its circumference is:

C = 2 \times \frac{22}{7} \times 14 = 88 \text{ inches}

Section 3

Finding Diameter from Circumference

Property

To estimate the diameter when given the circumference, use the rearranged circumference formula:

d = \frac{C}{\pi}

Since $\pi \approx 3.14$ , you can estimate: $d \approx \frac{C}{3.14}$