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Radius of A Circle: Definition and Examples | EDU.COM

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Radius of A Circle: Definition and Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Radius of A CircleRadius of A Circle: Definition and ExamplesTable of ContentsRadius of a Circle Definition of Radius of a Circle

The radius of a circle is the distance between the center of a circle and any point on its boundary (circumference). It is typically shown with the letter "rrr" or "RRR" in math problems. When we talk about one radius, we say "radius," but when talking about more than one, we use the term "radii." This important measurement can be found in many 3D shapes too, like spheres, cylinders, and cones that have circular bases.

The radius connects to other circle measurements through several formulas. We can find the radius if we know the diameter by dividing it by 2 (r=d2r = \frac{d}{2}r=2d​). If we know the circumference, we can use the formula r=C2πr = \frac{C}{2\pi}r=2πC​. For area, we can find the radius using r=Areaπr = \sqrt{\frac{Area}{\pi}}r=πArea​​. The equation of a circle with radius r and center at origin (0, 0) is given by x2+y2=r2x^2 + y^2 = r^2x2+y2=r2, while for a circle with center at point (h,k)(h, k)(h,k), the equation is (x−h)2+(y−k)2=r2(x-h)^2 + (y-k)^2 = r^2(x−h)2+(y−k)2=r2.

Examples of Radius of a Circle Example 1: Finding the Radius from a Wire Problem:

A wire measures 101010 units in length. Find the radius of a circle formed by bending the wire and joining its two ends? (Use π=3.14\pi = 3.14π=3.14).

Step-by-step solution: Step 1, Think about what happens when we bend the wire into a circle. The length of the wire becomes the circumference of the circle. Step 2, Write down the formula for circumference: C=2πrC = 2\pi rC=2πr Step 3, Substitute what we know: 10=2rπ10 = 2r\pi10=2rπ Step 4, Solve for radius: r=102πr = \frac{10}{2\pi}r=2π10​ Step 5, Calculate the answer: r=102×3.14=1.6r = \frac{10}{2 \times 3.14} = 1.6r=2×3.1410​=1.6 units Example 2: Finding the Radius from the Diameter Problem:

What is the radius of the given circle?

Finding the Radius from the Diameter

Step-by-step solution: Step 1, Look at the measurement shown in the circle. The diameter is 252525 inches. Step 2, Remember the formula that connects diameter and radius: Radius=Diameter2\text{Radius} = \frac{\text{Diameter}}{2}Radius=2Diameter​ Step 3, Substitute the known value: Radius=252\text{Radius} = \frac{25}{2}Radius=225​ Step 4, Calculate: Radius=12.5\text{Radius} = 12.5Radius=12.5 inches Example 3: Finding the Radius from the Area Problem:

A circular garden spans a region of 50.2450.2450.24 square feet. Find the radius.

Step-by-step solution: Step 1, Write down what we know: The area of the garden is 50.2450.2450.24 square feet. Step 2, Recall the formula for the area of a circle: Area=πr2\text{Area} = \pi r^2Area=πr2 Step 3, Rearrange the formula to solve for radius: r=Areaπr = \sqrt{\frac{\text{Area}}{\pi}}r=πArea​​ Step 4, Substitute our known values: r=50.243.14r = \sqrt{\frac{50.24}{3.14}}r=3.1450.24​​ Step 5, Simplify what's under the square root: r=16r = \sqrt{16}r=16​ Step 6, Calculate the final answer: r=4r = 4r=4 feet Comments(2)AAppDeveloperYuriNovember 4, 2025I've used this radius of a circle def. with my students. It's clear & the examples really helped them grasp the concept. Thanks!

PPotterBobNovember 4, 2025This glossary page on the radius of a circle is great! It's helped my students grasp the concept easily. Thanks for the clear def and examples!

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