Area of 3/4 Circle Support
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.
Area of 3/4 Circle Formula
The area of ¾ of a circle is equal to ¾ of the area of the whole circle.
So the area of three-quarters of a circle = ¾ πr2, where r is the radius of the circle.
Area of a 3/4 Circle Calculator
How the Calculator Works
- Select if you want to use the radius or diameter (default is radius).
- For the value, you can choose a whole number, decimal or fraction.
- You can type a fraction by typing the numerator then '/' then the denominator.
- You can type a mixed number by typing the whole-number part, then a space then the fraction part.
- Examples: 2 1/2 (two and one-half); 3 4/5 (three and four-fifths); 7 1/3 (seven and one-third).
- Choose your units of measurement (default is cm)
- Choose your desired accuracy (default is 2 decimal places)
- Click the Find Area button
- You will be given two answers for the area, one in terms of Pi (π) and the other answer as a decimal value.
Area of 3/4 Circle Examples
Example 1) Find the area of the sector below, giving your answer to 1 decimal place:
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:
\[ A = 21.2 \; cm^2 \; to \; 1\; decimal \; place \]
Example 2) Work out the area of the circular grass sector below, giving your answer to 2 decimal places.
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:
\[ A = 71.27 \; m^2 \; to \; 2\; decimal \; places \]
Example 3) Tyger makes a yellow logo for a T-shirt design shown below. Find the area of the yellow logo to 1dp.
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:
\[ A = 28.9 \; in^2 \; to \; 1\; decimal \; place \]
Area of 3/4 Circle Worksheets
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.
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Each calculator page comes with worked examples, formulas and practice worksheets.
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