To find the radius of a circle where its area and circumference are equal, we can start by using the formulas for the area and circumference.
The area (A) of a circle is given by the formula:
A = πr²
where r is the radius of the circle.
The circumference (C) of a circle is given by the formula:
C = 2πr
We want to find r such that:
πr² = 2πr
We can simplify this by dividing both sides by π (assuming π is not equal to zero):
r² = 2r
Next, we can rearrange the equation:
r² – 2r = 0
Now, we can factor this equation:
r(r – 2) = 0
This gives us two possible solutions:
r = 0 or r = 2
Since a radius of 0 does not make sense in this context, the only viable solution is:
r = 2
Therefore, the radius of the circle must be 2 units for its area and circumference to be equal.