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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.
Let r be the radius of the circle.
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.