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.
Things You'll Need
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 x pi x radius (r)
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 x 2 x pi x r
Since 0.5 x 2 = 1, you can write the equation this way:
SC = pi x r
Now solve the equation for r, since you are trying to solve for radius. Do this by dividing both sides by pi to get r by itself. The result is the following:
r = SC / pi
Finally, plug in the value you have been given for the circumference of the semicircle and the value of pi to calculate the radius. For example, if the semicircle has a circumference of 5 centimeters, the calculation would look like this:
r = 5 cm / 3.14 = 1.6 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 = 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 = 20 cm / 2 = 10 cm
Tips & Warnings
- Remember that *pi* is a constant that is equal to approximately 3.14.
- Photo Credit emarto/iStock/Getty Images
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