How to Find the Radius of a Semi Circle

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A semicircle is one half of a circle. It looks like a straight line with a circular arc connecting its ends to one another. The straight edge of the semicircle is the diameter and the arc is half the circumference of a full circle with the same diameter. You can find the radius of a semicircle using the formulas for circumference and diameter. Which formula you use will depend on what information you have been given to start.

Calculating the Radius of a Semicircle With a Known Circumference

    First, modify the formula for the circumference of a circle to reflect that you are dealing with a semicircle. The formula for the circumference of a circle (​C​) is as follows:

    C = 2\pi r

    Where ​r​ is the radius. Since a semicircle is one half of a circle, the circumference of a semicircle is half the circumference of a circle. The formula for the circumference of a semicircle (​SC​) is the formula for the circumference of a circle multiplied by one half, or 0.5.

    SC = 0.5 × 2 \pi r

    Since 0.5 × 2 = 1, you can write the equation this way:

    SC = \pi r

    Now solve the equation for ​r​, since you are trying to solve for radius. Do this by dividing both sides by π to get ​r​ by itself. The result is the following:

    r = \frac{SC}{\pi}

    Finally, plug in the value you have been given for the circumference of the semicircle and the value of π to calculate the radius. For example, if the semicircle has a circumference of 5 centimeters, the calculation would look like this:

    r = \frac{5 \text{ cm}}{3.14} = 1.6 \text{ cm}

Calculating the Radius of a Semicircle With a Known Diameter

    First, write the equation for the diameter of a circle, which is the same as the diameter of a semicircle. Since the diameter of a circle, or ​d​, is twice as long as the radius, or ​r​, the equation for diameter is the following:

    d = 2r

    Now rearrange the equation for the diameter of a circle to solve for radius. To solve for r, divide both sides by two. Doing so gives the following:

    r = \frac{d}{2}

    Finally, plug in the value that you have been given for the diameter of the semicircle. For example, if the diameter has a value of 20 cm the calculation would look like this:

    r = \frac{20 \text{ cm}}{2} = 10 \text{ cm}

    Tips

    • Remember that π is a constant that is equal to approximately 3.14.

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