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Math · Grade 7 Math

Chapter 7: Circles

Telling Area from Circumference

Which question is being asked.

Lesson
4
Time
About 18 minutes
0 of 7 done

Step 1: Let's Learn

Read it, or press Listen and follow the words.

Circumference measures around the edge. Area measures the space inside.

The two formulas

Circumference is 2πr. Area is πr². One uses the radius once, the other twice.

The units give it away

A fence is measured in metres, so it is circumference. Grass is measured in square metres, so it is area.

Words that signal each

Edging, fencing, and ribbon mean around. Painting, covering, and turf mean inside.

Which question is being asked

Fencing round a circular pond needs the circumference. Turf to cover it needs the area. Edging, ribbon and borders are circumference; paint, turf and material are area. Identify what is being covered or surrounded before choosing a formula.

The units confirm your choice

Circumference comes out in centimetres, area in square centimetres. If your answer to a fencing question carries square units, you used the wrong formula. Writing units on every answer turns this into an automatic check.

Some problems need both

A circular flower bed might need edging and soil, requiring circumference and area from the same radius. Calculate them separately and label each clearly — mixing the two mid-problem is easy when both start from the same number.

They do not scale together

Double the radius and the circumference doubles while the area quadruples. The two measurements grow at different rates, which is why a large pizza has proportionally less crust than a small one.

Step 2: Try It Yourself

Tap and try it out.

One circle, both measurements. Watch which one grows faster.
d = 8
  • Diameter8 cm
  • Circumference25.13 cm
  • Area50.27 cm²
  • Circumference ÷ diameter3.14

Circumference is a length, measured in cm. Area is a coverage, measured in cm². The units tell them apart.

Step 3: Watch an Example

One step at a time.

Watch Leo Pick the Right Formula

A circular pond of radius 3 m needs edging, and then needs covering.

  1. Step 1

    Edging goes around the outside, so that is circumference.

Step 4: Your Turn

Practice makes it stick.

The Fence

Problem 1 of 2

Fencing a circular garden. Which is needed? Answer 1 for circumference, 2 for area.

The Turf

Problem 2 of 2

Laying turf on that garden. Which is needed? Answer 1 for circumference, 2 for area.

Around or Inside

1 of 4

Ribbon around a cake. 1 for circumference, 2 for area.

2 of 4

Icing on top of a cake. 1 for circumference, 2 for area.

3 of 4

An answer in square metres. 1 for circumference, 2 for area.

4 of 4

Radius 5. What is 2r?

Step 5: Quick Check

Show what you know.

Question 1 of 1

Edging a round rug. 1 for circumference, 2 for area.

What You Learned

  • Circumference measures around the circle; area measures inside it.
  • Circumference is 2πr, area is πr².
  • The units asked for tell you which one is wanted.