120r. Review Circles and Circumference

Learning Intentions

• To know the meaning of the terms diameter, radius and circumference
• To understand that pi () is a number that equals the circumference of any circle divided by its diameter
• Solve the circumference of a circle Use a calculator
• find the circumference of a circle using an approximation for

Pre-requisite Summary

• Know that a circle is a closed shape where all points on the boundary are the same distance from the centre
• Understand that length is measured in one-dimensional units such as mm, cm and m
• Be able to multiply whole numbers and decimals
• Know how to Use a calculator for multiplication
• Understand that a formula is a rule for calculating a quantity
• Be able to Substitute a given number into a formula
• Know that an approximation is a value close to the exact value

Worked Examples

Worked Example 1

State the meaning of each term:

a) radius

b) diameter

c) circumference

Worked Example 2

Use circle facts to find the missing measure:

a) radius cm. Find the diameter

b) diameter mm. Find the radius

c) radius m. Find the diameter

Worked Example 3

Use a calculator to find the circumference:

a) diameter cm

b) radius cm

c) diameter m

Worked Example 4

Use to find the circumference:

a) diameter cm

b) radius cm

c) diameter mm

Worked Example 5

A circle has circumference cm using . Find the diameter.

Worked Example 6

A circle has radius cm.

a) Find the circumference using a calculator

b) Find the circumference using

Problems

Problem 1

State the meaning of each term:

a) radius

b) diameter

c) circumference

Problem 2

Use circle facts to find the missing measure:

a) radius cm. Find the diameter

b) diameter mm. Find the radius

c) radius m. Find the diameter

Problem 3

Use a calculator to find the circumference:

a) diameter cm

b) radius cm

c) diameter m

Problem 4

Use to find the circumference:

a) diameter cm

b) radius cm

c) diameter mm

Problem 5

A circle has circumference cm using . Find the diameter.

Problem 6

A circle has radius cm.

a) Find the circumference using a calculator

b) Find the circumference using

Exercises

Understanding and Fluency

Exercise 1.

State the meaning of each term:

a) radius

b) diameter

c) circumference

d) centre

Exercise 2.

Complete each statement:

a) The diameter is ______ times the radius

b) The radius is ______ the diameter

c) The circumference is the distance ______ a circle

Exercise 3.

Find the missing measure:

a) radius cm, diameter ?

b) diameter cm, radius ?

c) radius mm, diameter

d) diameter m, radius

Exercise 4.

Use a calculator to find the circumference:

a) diameter cm

b) radius cm

c) diameter cm

Exercise 5.

Use to find the circumference:

a) diameter cm

b) radius cm

c) diameter mm

Exercise 6.

Find the circumference of each circle:

a) radius cm, using a calculator

b) radius cm, using a calculator

c) diameter m, using

Exercise 7.

Use to find the missing measure:

a) circumference cm, diameter ?

b) circumference cm, radius ?

c) circumference mm, diameter ?

Exercise 8.

Choose the correct formula and Evaluate:

a) circumference when the diameter is known

b) circumference when the radius is known

c) diameter when the radius is known

Reasoning

Exercise 9.

Explain why the diameter of a circle is always twice the radius.

Exercise 10.

A student says that is different for different circles because large circles have larger circumferences. Explain the mistake.

Exercise 11.

Noah says that circumference is measured in square centimetres because a circle is a two-dimensional shape. Is he correct? Explain.

Exercise 12.

Explain why and are equivalent formulas.

Exercise 13.

A student uses to find the circumference. Describe the error.

Problem-solving

Exercise 14.

A bicycle wheel has diameter cm. Find its circumference using .

Exercise 15.

A circular table has radius m. Find its circumference using a calculator.

Exercise 16.

A hoop has circumference cm using . Find its diameter.

Exercise 17.

A circular pond has radius m. Find the circumference using .

Exercise 18.

A clock face has diameter cm. Find the circumference using both a calculator and .

Exercise 19.

A circle has circumference mm using . Find its radius.

Potential Misunderstandings

• Students may confuse radius and diameter
• Students may forget that the diameter is twice the radius
• Students may think circumference means the space inside the circle rather than the distance around it
• Students may think is measured in units rather than being a number
• Students may think changes from one circle to another
• Students may use the wrong formula, such as instead of or
• Students may forget to double the radius before using
• Students may use square units for circumference instead of linear units
• Students may round too early when using a calculator
• Students may confuse using an exact calculator value of with using an approximation such as

Next: 121r. Review Area of Shapes and Composite Figures