Area of 1/4 Circle Support

Welcome to our Area of 1/4 Circle Support page.

We explain how to find the area of one-quarter 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 1/4 Circle Formula

The area of ¼ of a circle is equal to ¼ of the area of the whole circle.

area of circle one quarter circle formula image

So the area of one-quarter of a circle = ¼ πr2, where r is the radius of the circle.

Area of a 1/4 Circle Calculator

Area of a 1/4 Circle Calculator

Answer1


Answer2

 
 

How the Calculator Works

area of 1/4 circle formula image

  1. Select if you want to use the radius or diameter (default is radius).
  2. 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).
  3. Choose your units of measurement (default is cm)
  4. Choose your desired accuracy (default is 2 decimal places)
  5. Click the Find Area button
  6. 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 1/4 Circle Examples

Example 1) Find the area of the sector below, giving your answer to 1 decimal place:

area of 1-4 circle example 1

The sector of the circle shown is a ¼ circle.

The area of ¼ circle is equal to ¼ of the area of the whole circle.

So the area of the sector is:

\[ A = {1 \over 4} \pi r^2 \]

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

We know that the radius is 8 cm, so we if we input this value into the formula, we get:

\[ A = {1 \over 4} \pi (8)^2 \]

We need to work out the brackets first.

\[ (8)^2 = 8 \times 8 = 64 \]

This gives us:

\[ A = {1 \over 4} \pi (64) \]

If we multiply the ¼ by 64 we get:

\[ A = 16 \pi \]

So this gives us:

\[ A = 50.3 \; cm^2 \; to \; 1\; decimal \; place \]

Example 2) Work out the area of the sector below, giving your answer to 2 decimal places.

area of 1-4 circle example 2

The sector shown is a ¼ circle.

The area of ¼ circle is equal to ¼ of the area of the whole circle.

So the area of the sector is:

\[ A = {1 \over 4} \pi r^2 \]

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

We know that the radius is 4 ½ inches, so we if we input this value into the formula, we get:

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

We need to work out the brackets first.

\[ (4 {1 \over 2})^2 = 4 {1 \over 2} \times 4 {1 \over 2} = {81 \over 4} \]

This gives us:

\[ A = {1 \over 4} \pi ({81 \over 4}) \]

If we multiply the fractions gives us:

\[ A = {81 \over 16} \pi \]

So this gives us:

\[ A = 15.90 \; in^2 \; to \; 2\; decimal \; places \]

Example 3) Frazer makes 4 quarter-circlular flower beds in his garden as shown below. What is the area of each bed? Give your answer to 1 decimal place.

area of 1-4 circle example 3

Each flowerbed is shown is a ¼ circle.

So the area of each flowerbed is:

\[ A = {1 \over 4} \pi r^2 \]

The radius of the circle is not shown, but we can see that the diameter of the circle (the distance from one side to the other) is equal to 15 m.

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

\[ r = {d \over 2} = {15 \over 2} m \]

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

\[ A = {1 \over 4} \pi ({15 \over 2})^2 \]

We need to work out the brackets first.

\[ ({15 \over 2})^2 = {15 \over 2} \times {15 \over 2} = {225 \over 4} \]

This gives us:

\[ A = {1 \over 4} \pi ({225 \over 4}) \]

If we multiply the fractions gives us:

\[ A = {225 \over 16} \pi \]

Multiplying this fraction by π gives us:

\[ A = 44.2 \; m^2 \; to \; 1\; decimal \; place \]

Area of 1/4 Circle Worksheets

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

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

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

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