Lesson 14 — Activity 4: Measuring the Diameter and Radius of Circles



Getting Ready


Now that you have practised determining the circumference of circles, you will learn to calculate other distances within circles.


                  

Courtesy of ADLC

Think about This:

Diameter is the distance from a point along one edge of the circle, through the centre of the circle, to a point on the opposite side of the circle.

Radius is the distance from a point along the edge of the circle to the exact centre of the circle. Radius is half the value of the diameter.





Sometimes you may be asked to find either the diameter or the radius. Once again, we can use formulas to find out the answer.


There are two ways to find the diameter of a circle.


1. If you have been given the radius of the circle, to find the diameter, multiply the radius by 2.


For example, if you know the radius of a circle is 15 mm and are asked to find the diameter, you would multiply 15 by 2.


The diameter of a circle with a radius of 15 mm is 30 mm.



2. The other way you can find the diameter of a circle is when you are given the circumference. To solve this, you must first rearrange the equation for circumference so that you are now finding the diameter.

The rearranged equation is

d = C
       π


For example, if a circle has a circumference of 36 cm, you would do the following:

d = C
       π


d = 36
     3.14


d = 11.46 cm


The circle has a diameter of 11.46 cm.



There are two ways to find the radius of a circle.

1. If you have been given the diameter of a circle, to find the radius, divide the diameter by 2.

For example, if you know the diameter of a circle is 26 cm and are asked to find the radius, you would divide 26 by 2.

The radius of a circle with a diameter of 26 cm is 13 cm.

2. The other way you can find the radius of a circle is when you are given the circumference. To solve this, you must first rearrange the equation for circumference so that you are now finding the radius.

The rearranged equation is

r = C
     2π

For example, if a circle has a circumference of 24 cm, you would do the following:

r = C
     2π

r = 24
        2 x 3.14

r = 3.82 cm

The circle has a radius of 3.82 cm.




Try This:

Solve these problems. Use the formulas above and a calculator to solve.



1. A glass installer measured a window and calculated that it has a circumference of 18.84 metres. What is the window's diameter?




2. The buttons on Sage's blouse each have a diameter of 6 millimeters. What is each button's radius?

Courtesy of Pixabay

 

1. For the window:


d = C
       π


d = 18.84
         3.14


d = 6 m

The window's diameter is 6 m.



2. For the blouse:

6 ÷ 2 = 3

Each button has a radius of 3 mm.




  Self-check!

Try This!

Try this activity to further practice finding the circumference, diameter, and radius of a circle. Round all answers to one decimal place.


What is the circumference of a circle with a radius of 2 km?

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The circumference of this circle is 12.6 kilometres.


What is the radius of a circle with a circumference of 100 m?

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The radius of this circle is 15.9 metres.


What is the diameter of a circle that has a circumference of 200 mm?

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The diameter of this circle is 63.7 milimetres.





Digging Deeper

 

Click here to play a game on finding circumference, diameter, and radius of circles.