Find Circumference and Area of a Circle

Students derive and apply the formulas for the circumference (C = πd = 2πr) and area (A = πr²) of a circle. They solve problems involving circles in real-world contexts and work with both exact (π) and approximate (3.14 or 22/7) values.

Try three of them

Real questions from this skill, graded here. No account, and nothing is saved.

Grade 7 · Geometry · question 1 of 3

0 of 20

20 rungs. A star at the top.

A = 3.14 × 3^2 =

How it is taught

0:00 of 3:58

Circumference is the distance around a circle.

It is 2 times pi times the radius.

Pi is about 3.14.

Read it: Circumference and area of a circle

This circle's diameter is 10, so its radius is 5. The circumference is about 3.14 diameters long: C = 3.14 × 10 = 31.4. The area uses the radius twice: A = 3.14 × 5 × 5 = 78.5 square units.

For the circumference, multiply the diameter by 3.14.
For the area, multiply the radius by itself, then by 3.14.
Given the radius, double it for the diameter: 2 × 5 = 10.

Around any circle, the circumference is about 3.14 diameters long. That number is called π.

The radius reaches from the center to the edge, half the diameter: 10 ÷ 2 = 5.

Area counts square units, so it uses the radius twice: 5 × 5 = 25, and 3.14 × 25 = 78.5.

C = 3.14 × d, and A = 3.14 × r × r.

Using the radius for the circumference: 3.14 × 5 = 15.7.

C uses the diameter: 3.14 × 10 = 31.4. Only A uses r × r.

d = 14: C = 3.14 × 14 = ___ — 43.96. The circumference is about 3.14 diameters long: 3.14 × 14 = 43.96.

Pizza with r = 5 in

Here's a round pizza with a radius of five inches. We want to find the distance around it, and how much pizza is inside.

Grade 7 · Circumference and area of a 5-inch radius pizza

Here's the circle. The radius — from the center to the edge — is five inches.

The distance around the edge of a circle is called the circumference.

The formula is C equals two times pi times r.

Plug in five for r: two times pi times five.

Two times five is ten, so C equals ten pi — about thirty-one point four inches.

Next, the area — how much space is inside the circle.

The formula is A equals pi times r squared.

Five squared is twenty-five, so A equals pi times twenty-five.

That comes out to about seventy-eight point five square inches.

So a five-inch pizza is about thirty-one inches around and seventy-eight square inches of pizza. Yum!

Now you try. Find the diameter of this circle. What is the diameter?

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

More of the library

Every skill has a page

Practise this skill free

14 days of every skill, practice packets, Fluency sheets and up to four students. No card.

Start free