The four different ways to find the radius of a circle are shown below:
In a circle, the radius is always half the length of its diameter.
r = d / 2
Example #1:
Find the radius if the diameter is 20 inches
r = d / 2 = 20 / 2 = 10
The radius is 10 inches.
The example below illustrates clearly how to find the radius of a circle when the circumference is known.
Example #2:
Suppose the circumference of a circle is 50.24 inches. Find the radius, r.
The radius is 8 inches when the circumference is 50.24 inches
The formula to find the area of a circle is A = πr^{2}
Example #3:
Find the radius if the area of the circle is equal to 50 cm^{2}
A = πr^{2}
Substitute 50 for A
50 = πr^{2}
Substitute 3.14 for π
50 = 3.14r^{2}
Divide both sides of the equation by 3.14
50 ÷ 3.14 = (3.14 ÷ 3.14)r^{2}
15.92 = (1)r^{2}
15.92 = r^{2}
r = √(15.92)
r = 3.98
The radius is 3.98 cm
The formula to find the area of a sector is A = (n^{0} / 360^{0})πr^{2}
n^{0} is the measure of the central angle
Example #4:
Find the radius if the central angle is 90 degrees and the area of the sector is equal to 19.63 cm^{2}
A = (n^{0} / 360^{0})πr^{2}
Substitute 19.63 for A
19.63 = (n^{0} / 360^{0})πr^{2}
Substitute 90 degrees for n^{0}
19.63 = (90^{0} / 360^{0})πr^{2}
19.63 = (0.25)πr^{2}
19.63 = 0.785r^{2}
Divide both sides by 0.785
19.63 ÷ 0.785 = (0.785 ÷ 0.785)r^{2}
25.0063 = (1)r^{2}
25.0063 = r^{2}
r = √(25.0063)
r = 5
Sep 30, 22 04:45 PM