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Quarter Circle: Definition and Examples | EDU.COM

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Quarter Circle: Definition and Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Quarter CircleQuarter Circle: Definition and ExamplesTable of ContentsQuarter Circle Definition of Quarter Circle

A quarter circle is one-fourth part of a complete circle. In mathematical terms, it is the area created by two perpendicular radii and one-fourth of the circumference of a whole circle. This shape can also be referred to as a quadrant. You can visualize a quarter circle as the shape formed when you cut a pizza into four equal slices.

The area of a quarter circle is one-fourth the area of the whole circle, which is expressed as πr24\frac{\pi r^2}{4}4πr2​, where rrr is the radius of the circle. The perimeter of a quarter circle consists of two radii and one-fourth of the circle's circumference, giving us the formula 2r+πr22r + \frac{\pi r}{2}2r+2πr​, where rrr represents the radius.

Examples of Quarter Circle Example 1: Finding the Area of a Quarter Circle Problem:

If the radius of a circle is 666 cm, what will be the area of a quarter of its circle?

Step-by-step solution:

Step 1, Recall the formula for the area of a quarter circle. The area equals πr24\frac{\pi r^2}{4}4πr2​.

Step 2, Put the given radius value into the formula. We know that r=6r = 6r=6 cm and π=3.14\pi = 3.14π=3.14.

Step 3, Calculate the area by substituting these values.

Area of a quadrant=πr24=3.14×6×64=113.044=28.26 cm2\text{Area of a quadrant} = \frac{\pi r^2}{4} = \frac{3.14 \times 6 \times 6}{4} = \frac{113.04}{4} = 28.26 \text{ cm}^2Area of a quadrant=4πr2​=43.14×6×6​=4113.04​=28.26 cm2

Example 2: Finding the Area with Given Diameter Problem:

If the diameter of a circle is 32 cm32 \text{ cm}32 cm, what will be the area of a quarter circle?

Step-by-step solution:

Step 1, Find the radius from the diameter. Remember that radius=diameter2\text{radius} = \frac{\text{diameter}}{2}radius=2diameter​.

Step 2, Calculate the radius value. Radius=322=16 cm\text{Radius} = \frac{32}{2} = 16 \text{ cm}Radius=232​=16 cm

Step 3, Use the formula for the area of a quarter circle: πr24\frac{\pi r^2}{4}4πr2​.

Step 4, Calculate the area by substituting the values.

Area of quadrant=πr24=3.14×16×164=200.96 cm2\text{Area of quadrant} = \frac{\pi r^2}{4} = \frac{3.14 \times 16 \times 16}{4} = 200.96 \text{ cm}^2Area of quadrant=4πr2​=43.14×16×16​=200.96 cm2 Example 3: Finding the Perimeter of a Quarter Circle Playground Problem:

A circular park has a radius of 353535 yards. One-quarter of the park has a playground for toddlers. Find the perimeter of the playground.

Step-by-step solution:

Step 1, Identify what we're looking for. We need the perimeter of a quarter circle playground with radius 353535 yards.

Step 2, Recall the formula for the perimeter of a quarter circle: Perimeter=2r+πr2\text{Perimeter} = 2r + \frac{\pi r}{2}Perimeter=2r+2πr​

Step 3, Put the radius value into the formula. We know that r=35r = 35r=35 yards and π=3.14\pi = 3.14π=3.14.

Step 4, Calculate the perimeter.

Perimeter=2×35+3.14×352=70+54.95=124.95 yards\text{Perimeter} = 2 \times 35 + \frac{3.14 \times 35}{2} = 70 + 54.95 = 124.95 \text{ yards}Perimeter=2×35+23.14×35​=70+54.95=124.95 yards Comments(3)DDancerOliviaNovember 6, 2025This glossary def of quarter circle is great! I've used it to help my students grasp the concept, & the area formula explanation is super clear.

GGamerBobNovember 4, 2025I've used this quarter circle def. with my students. It's clear & the examples helped them grasp area & perimeter calcs. Great resource!

NNatureLover25September 17, 2025I’ve used this page to explain quarter circles to my kids, and it’s so clear! The formula and examples helped them grasp the concept quickly. Perfect for homework support!

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