Find the radius of a circle so that its area and circumference are the same.
Solution:
Circumference of the circle or perimeter of the circle is the measurement of the boundary of the circle.
Whereas the area of the circle defines the region occupied by it.
If we open a circle and make a straight line out of it, then its length is the circumference.
Let R be the radius of the circle.
Then the circumference of the circle is 2R
The area of a circle is πR2
If the area of a circle = circumference of the circle
πR2 = 2πR
R2 - 2R = 0
R( R - 2) = 0
R = 0 and R - 2 = 0
And R - 2 = 0
⇒ R = 2
Hence,
The radius of the circle
R = 0 and R = 2
Neglecting R = 0 as the point circle trivially has area and circumference the same.
Therefore,
The radius of the circle is R = 2 units
Find the radius of a circle so that its area and circumference are the same.
Summary:
The value of radius is 2 units for which area and circumference are the same.