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Math Lesson Guide

How to Calculate the Area of a Circle

A step-by-step tutor walkthrough of the circle area formula with real examples, common mistakes to avoid, and practice problems you can try yourself.

The Circle Area Formula

The area of any circle is found with one simple formula. Your tutor will always start here before diving into problems.

A = πr²

A = Area of the circle
π (pi) ≈ 3.14159…
r = Radius (distance from centre to edge)

Tutor tip: If a problem gives you the diameter instead of the radius, just divide it by 2 first. The radius is always half the diameter.

Worked Example: Find the Area Step by Step

Let’s walk through a classic problem the way an EDU-TAINMENT tutor would guide you in a session.

Problem

A circular garden has a radius of 7 metres. What is its area? Use π = 22/7.

1

Write the formula

Start every circle-area question by writing the formula down. It keeps your work organised and earns method marks.

A = πr²
2

Substitute the values

Replace π with 22/7 and r with 7. Notice the radius is 7, so r² = 7 × 7 = 49.

A = (22/7) × 7²
3

Simplify

7² = 49. Now you have (22/7) × 49. The 7 in the denominator cancels with one 7 from 49, leaving 22 × 7.

A = 22 × 7 = 154

State the final answer with units

Always include units squared. Area is two-dimensional.

A = 154 m²

Common Mistakes to Avoid

Our tutors see these errors every week. Here is how to avoid them.

Forgetting to square the radius

Students sometimes write πr instead of πr². Remember: the little 2 means multiply the radius by itself.

Using diameter as radius

If the problem says the diameter is 10 cm, the radius is 5 cm. Always halve the diameter first.

Forgetting units squared

Area is always in square units (cm², m², etc.). Length is cm; area is cm².

Mixing up π approximations

Some questions say 'use π = 22/7', others say 'use 3.14', and some want the exact answer in terms of π. Read the question carefully.

Practice Problems

Try these yourself, then reveal the tutor’s solution to check your work.

Problem 1 — Easy

Find the area of a circle with radius 5 cm. Use π = 3.14.

Problem 2 — Medium

A circular pond has a diameter of 14 m. What is its area? Use π = 22/7.

Problem 3 — Hard

A pizza has an area of 154 cm². What is its radius? Use π = 22/7.

Quick Reference Table

Handy values for common radii. Your tutor can help you memorise the patterns.

RadiusArea (πr²)Approximate (π ≈ 3.14)
1 unitπ units²3.14 units²
2 unit units²12.56 units²
3 unit units²28.26 units²
5 unit25π units²78.50 units²
7 unit49π units²153.86 units²
10 unit100π units²314.00 units²

Still stuck on circles?

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