E2.5 · Explain and use the circle-area formula

Ontario Grade 7 Mathematics

Spatial Sense

Ontario Grade 7 Mathematics · E2.5

What you will learn

• Identify the radius of a circle.
• Explain what the circle-area formula means.
• Use the formula to find the area of a circle and include square units.

1. Start with the radius

• The radius goes from the centre to the edge.
• The diameter goes all the way across through the centre.
• Radius is half of diameter.

2. Why the circle-area formula makes sense

• The circle's area is found using its radius.
• Pi, written as the Greek letter pi, is about 3.14.
• Radius squared means radius multiplied by itself.

3. Use the formula carefully

• Find or confirm the radius first.
• Multiply the radius by itself before multiplying by pi.
• Use square units for area.

4. Check your result

• Check the measurement used in the formula.
• Check the order of your operations.
• Check that the final units are square units.

Worked example

Example 1: Radius given

1. Use the radius
   The given measurement is already the radius, so substitute 5 cm for the radius in the formula.
   $$A=3.14(5)^2$$
2. Square the radius
   Squaring 5 means multiplying 5 by 5. This gives 25.
   $$5^2=25$$
3. Multiply and label
   Multiply 3.14 by 25. Since the measurement was in centimetres, the area is in square centimetres.
   $$A=78.5\text{ cm}^2$$

Worked example

Example 2: Diameter given

1. Find the radius
   The diameter is twice the radius. Divide the diameter by 2 to find the radius needed for the formula.
   $$r=12\div 2=6\text{ m}$$
2. Substitute the radius
   Use 6 m as the radius. Square it before multiplying by 3.14.
   $$A\approx 3.14(6)^2$$
3. Calculate the area
   Six squared is 36, and 3.14 times 36 is 113.04. The area uses square metres.
   $$A\approx 113.04\text{ m}^2$$

Worked example

Example 3: Compare two circle areas

1. Find the first area
   Use the 4 cm radius in the circle-area formula. Square the radius, then multiply by 3.14.
   $$A_1\approx 3.14(4)^2=50.24\text{ cm}^2$$
2. Find the second area
   Repeat the same process with the 7 cm radius. Keeping the same value of pi makes the areas fair to compare.
   $$A_2\approx 3.14(7)^2=153.86\text{ cm}^2$$
3. Compare the areas
   Subtract the smaller area from the larger area to find how much greater the larger area is.
   $$153.86-50.24=103.62\text{ cm}^2$$

Common mistakes and how to avoid them

Lesson summary

• The radius is the distance from a circle's centre to its edge.
• Use the circle-area formula: area equals pi times radius squared.
• Use 3.14 as an approximation for pi when instructed.
• If given the diameter, divide it by 2 to find the radius.
• Write the answer in square units.

Check your understanding

Key terms

Area

The amount of flat space inside a shape.

Centre

The point in the middle of a circle.

Radius

The distance from a circle's centre to its edge.

Diameter

The distance across a circle through its centre; it is twice the radius.

Pi

A number used in the circle-area formula. It is about 3.14.

Squared

A number multiplied by itself.

Continue through Grade 7 Math

View the complete Grade 7 Math Ontario Grade 7 Mathematics curriculum and lessons

• E2.4 · Construct circles from a radius, diameter, or circumference
• E2.6 · Use cylinder nets to calculate surface area
• E1.1 · Classify cylinders, pyramids, and prisms by properties and symmetry
• E1.2 · Draw scaled top, front, side, and perspective views
• E1.3 · Perform dilations and describe similar shapes
• E1.4 · Translate, reflect, and rotate shapes on a Cartesian plane

About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Ontario Grade 7 Mathematics, expectation E2.5. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

Official curriculum reference

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