What is the Radius of a Circle?
The radius of a circle is the distance between the fixed point(center) and any point on the circumference of the circle.
The radius can be easily calculated by considering half the length of the diameter of a circle.
Formula to Find the Radius of a Circle
Formula for the Radius of a Circle, When the Diameter is Given:
Diameter = 2 \(\times\) Radius
D = 2r
Hence, Radius, r = \(\frac{D}{2}\)
Formula for the Radius of a Circle, When the Circumference is Given:
Circumference C = 2 \(\times\) π \(\times\) Radius
C = 2πr
r = \(\frac{C}{2\pi}\)
Formula for the Radius of a Circle, When the Area is Given:
Area = π \(\times~\text{Radius}^2\)
A = π\(r^2\)
r = \(\sqrt{\frac{A}{\pi}}\)
Solved Examples
Example 1: Find the radius of a circle if its diameter is 44 meters.
Solution:
The diameter of the circle is provided as, D= 44 m.
Radius of the circle is calculated by the formula,
Radius, r = \(\frac{D}{2}\)
= \(\frac{44}{2}\)
= 22 m
So, the radius of the circle is 22 meters.
Example 2: Find the radius of the circle, if the circumference is 66 inches.[Use π = \(\frac{22}{7}\)].
Solution:
The circumference of the circle is, C = 66 in.
Radius of the circle is calculated using the formula,
r = \(\frac{C}{2\pi}\)
r = \(\frac{66\times 7}{22\times 2}\)
r = \(\frac{21}{2}\)
r = 10.5 in
So, the radius of the circle is 10.5 inches.
Example 3: Find the radius of the circle, if its area is 154 square yards.
Solution:
The area A of the given circle is stated as 154 square yards.
Radius of a circle is obtained by applying the formula,
r = \(\sqrt{\frac{A}{\pi}}\)
r = \(\sqrt{\frac{154\times 7}{22}}\)
r = \(\sqrt{7\times 7}\)
r = \(\sqrt{7^2}\)
r = 7 in.
So, the radius of the circle is 7 inches.
Example 4: Jacob has ordered pizza. After the pizza was delivered he read that the pizza has an area of 49 square centimeters. Now he wants to calculate the length of the boundary of the pizza. Can you help him?(Use = \(\frac{22}{7}\))
Solution:
Area of the pizza is stated in the question as, A = 49\(\pi cm^2\)
Radius of the circle is calculated by the formula,
r = \(\sqrt{\frac{A}{\pi}}\)
r = \(\sqrt{\frac{49\pi}{\pi}}\)
r = \(\sqrt{49}\)
r = 7 cm
Hence, the radius of the pizza is 7 centimeters.
Circumference of the pizza, C = 2πr
C = \(2\times \frac{22}{7}\times 7\)
C = 22 \(\times\) 2
C = 44 cm
So, the length of the boundary of the pizza is 44 centimeters.
A circle is a locus of points that move in such a way that the distance from a fixed point always remains the same.
The radius is half of the diameter of a circle.
The circumference of a circle increases when the radius increases.
The area of a circle is the space enclosed by its boundary. Having said this, the area of a circle increases when the radius is increased.
No, a polygon is made by only line segments, but a circle is a curved and closed shape.