E2.4 · Construct circles from a radius, diameter, or circumference

Ontario Grade 7 Mathematics

Spatial Sense

Use a radius, diameter, or circumference to make a circle

What you will learn

• Identify the centre, radius, diameter, and circumference of a circle.
• Construct a circle when its radius or diameter is given.
• Use circumference to find a circle’s diameter, then construct the circle.

1. Meet the parts of a circle

• The radius goes from the centre to the edge.
• The diameter goes across the circle through the centre.
• The circumference is the distance around the circle.

2. Construct from a radius or diameter

• Set the compass opening to the radius.
• If given a diameter, divide its length by 2 before setting the compass.
• Keep the compass point on the centre as you turn it.

3. Construct from a circumference

• Use circumference divided by 3.14 to estimate diameter.
• Divide the diameter by 2 to get the radius for the compass.
• A circumference-based construction is an estimate when using 3.14.

4. Check and practise your construction

• Check which measurement the question gives you.
• Find the radius before setting the compass.
• Keep units with measurements and label the centre and radius.

Worked example

Given the radius

1. Set the compass
   The given radius is the distance from the centre to the circle’s edge. Set the compass opening to 3 cm using a ruler.
   $$r=3\text{ cm}$$
2. Draw and label
   Mark a centre point. Place the compass point there and turn the pencil end around once. Label the centre O and one radius as 3 cm.

Worked example

Given the diameter

1. Find the radius
   The diameter is two radii across. Find half of 8 cm so the compass is set to the distance from the centre to the edge.
   $$r=8\div2=4\text{ cm}$$
2. Draw the circle
   Set the compass opening to 4 cm. Mark a centre point, place the compass point on it, and turn the pencil end around to make the circle. Label one radius 4 cm.

Worked example

Given the circumference

1. Estimate the diameter
   Circumference is about 3.14 times diameter. Divide the given circumference by 3.14 to estimate the diameter.
   $$d\approx37.68\div3.14=12\text{ cm}$$
2. Find the radius
   The radius is half the diameter. Set the compass opening to this radius.
   $$r=12\div2=6\text{ cm}$$
3. Construct
   Use a ruler to set a 6 cm compass opening. Place the compass point at the centre and turn the pencil around to draw the circle. Label the radius 6 cm.

Common mistakes and how to avoid them

Lesson summary

• A radius runs from the centre to the edge; a diameter goes across the circle through its centre.
• Use the radius as the compass opening.
• From a diameter, find the radius by dividing by 2.
• From a circumference, estimate the diameter by dividing by 3.14, then divide by 2 to find the radius.

Check your understanding

Key terms

Circle

A round shape whose edge is the same distance from its centre at every point.

Centre

The fixed middle point of a circle.

Radius

A straight distance from the centre of a circle to its edge.

Diameter

A straight distance across a circle through its centre.

Circumference

The distance all the way around a circle.

Compass

A drawing tool used to make circles with a chosen radius.

Continue through Grade 7 Math

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

• E2.3 · Connect radius, diameter, and circumference
• E2.5 · Explain and use the circle-area formula
• 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 E2.4. 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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