Find the radius of a circle so that its area and circumference have the same value.

A circle is a two-dimensional curved plane. Every point on the circle is equidistant from the center.

Answer: The radius of the circle is 2 units so that its area and circumference have the same value.

Let's find the radius of the circle.

Explanation:

We know that the length of the circle is called the circumference. Also, the area enclosed inside the circumference is the area of the circle.

Let r be the radius of the circle.

Given that

area of the circle = circumference of the circle.

⇒ π r² = 2 π r

⇒ π r² - 2 π r = 0

⇒ π (r² - 2 r) = 0

By solving the equation using factorization method, we get

⇒ r (r - 2) = 0

Thus, we have two values of r. i.e., r = 0, 2

Neglecting r = 0 as a circle can not be formed with a radius measuring 0 units.

Thus, the value of the radius is 2 units which makes the area and circumference of the circle equal.