Question

If the circumference and area of circle are numerically equal . Then the diameter is equal to :

• A. area of the circle
• B. $\frac{\pi }{2}$
• C. $2\pi$
• D. $4$

Answer 1

The correct option is D $4$

Let $r$ be the radius of the circle.

Then, circumference of a circle $=2\pi r$$

and area of a circle $=\pi r^2$.

Given, circumference and area are equal.

Then, $2\pi r=\pi r^2$

$⟹$ $r=2$.

We know, diameter $=2r$.

Therefore, diameter $=2\left(2\right)=4$.

Hence, option $D$ is correct.