Welcome to our Area of 3/4 Circle Support page.

We explain how to find the area of three quarters of a circle and provide a quick calculator to work it out for you, step-by-step.

We also have several worksheeets and worked examples to help you practice and learn this skill.

The area of ¾ of a circle is equal to ¾ of the area of the whole circle.

The sector of the circle shown is a ¾ circle.

The area of ¾ circle is equal to ¾ of the area of the whole circle.

So the area of the sector is:

\[ A = {3 \over 4} \pi r^2 \]

where A is the area of the sector, and r is the radius of the circle

We know that the radius is 3cm, so we if we input this value into the formula, we get:

\[ A = {3 \over 4} \pi (3)^2 \]

We need to work out the brackets first.

\[ (3)^2 = 3 \times 3 = 9 \]

This gives us:

\[ A = {3 \over 4} \pi (9) \]

If we multiply the ¾ by 9 we get:

\[ A = {27 \over 4} \pi \]

Multiplying this fraction by π gives us:

\[ A = 21.2 \; cm^2 \; to \; 1\; decimal \; place \]

The area of ¾ circle is equal to ¾ of the area of the whole circle.

So the area of the sector is:

\[ A = {3 \over 4} \pi r^2 \]

where A is the area of the sector, and r is the radius of the circle

We know that the radius is 5 ½ meters, so we if we input this value into the formula, we get:

\[ A = {3 \over 4} \pi (5 {1 \over 2})^2 \]

We need to work out the brackets first.

\[ (5 {1 \over 2})^2 = 5 {1 \over 2} \times 5 {1 \over 2} = {121 \over 4} \]

This gives us:

\[ A = {3 \over 4} \pi ({121 \over 4}) \]

If we multiply the fractions gives us:

\[ A = {363 \over 16} \pi \]

Multiplying this fraction by π gives us:

\[ A = 71.27 \; m^2 \; to \; 2\; decimal \; places \]

The sector of the circle shown is a ¾ circle.

So the area of the sector is:

\[ A = {3 \over 4} \pi r^2 \]

The radius of the circle is not shown, but we can see that the diameter (the distance from one side to the other) is equal to 7 inches.

The radius is equal to half of the diameter, so:

\[ r = {d \over 2} = {7 \over 2} inches \]

If we input this value into the formula, we get:

\[ A = {3 \over 4} \pi ({7 \over 2})^2 \]

We need to work out the brackets first.

\[ ({7 \over 2})^2 = {7 \over 2} \times {7 \over 2} = {49 \over 4} \]

This gives us:

\[ A = {3 \over 4} \pi ({49 \over 4}) \]

If we multiply the fractions gives us:

\[ A = {147 \over 16} \pi \]

Multiplying this fraction by π gives us:

\[ A = 28.9 \; in^2 \; to \; 1\; decimal \; place \]

We have created two worksheets for you to practice the skills shown on this page.

The first sheet involves finding the area of a range of ¾ circles in different units, where the radius is given.

The second sheet involves finding the area of ¾ circles, where either the radius or diameter are given.

Take a look at some more of our worksheets similar to these.

We have a range of area and volume calculators to help you find the area and volumes of a range of different 2d and 3d shapes.

Each calculator page comes with worked examples, formulas and practice worksheets.

We have a range of other area worksheets and support pages for a range of different 2d shapes.

We have a wide range of free math calculators to help you.

Most of our calculators show you their working out so that you can see exactly what they have done to get the answer.

Our calculator hub page contains links to all of our calculators!

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