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Pi & Its Application in Circles

What is Pi?

Pi (or   ) is a number with a practically infinite number of decimal places. It represents the ratio between a circle’s circumference and its diameter. Pi is equal to 3.14159 to 5 decimal places. Using pi we can calculate the are and circumference of a circle. Here are some more decimal places of Pi: 3.14159265358979323846

Using Pi to find Area

Using pi, we can find the area of a circle. There are three formulas depending on if you want to calculate the area using the diameter, radius or circumference.

Using the Radius

Using the Diameter

Using the Circumference

Here are some examples of these rules in action.
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Example 1 Find the area of the circle with a radius of 3 cm. Using the formula for the radius, we were able to calculate the area of the circle. The area of the circle is 28.3 cm². You can usually give your answer in terms of pi (more accurate) or in decimals.
3 cm
Example 2 Find the area of the circle with a diameter of 5 cm. Using the formula for the diameter, we were able to calculate the area of the circle. The area of the circle is 50.3 cm². We just had to       substitute the diameter into the formula.
8 cm
Example 3 Find the area of the circle with a circumference of 16 cm. Using the formula for the circumference, we were able to calculate the area of the circle. The area of the circle is 20.4 cm². We just had to substitute the circumference into the formula.
16 cm

Using Pi to find Circumference

We can also use pi to find the circumference of a circle. Here is the formula for this. In the example underneath we have calculated the circumference of a circle using the diameter and pi.
Example 3 Find the circumference of the circle. Using the formula, pi and the diameter of the circle we were able to find the circumference. The circumference of the circle is 15.7 cm.
5 cm

More Maths Topics

Now you should be quite familiar with pi and how to use it to find the area and circumference of a circle. You should have a look at some other topics on Ultimate Maths such as trigonometry. You can also select another topic in our library. Please share this page if you like it or found it helpful!
Angles Area & Perimeter Trigonometry
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Chapter 29:  Learning Outcomes Students will be introduced to pi! Students will learn how to use pi to find the area of a circle! Students will learn how to use pi to find the circumference of a circle!

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