Question

If the perimeter and the area of a circle are numerically equal, then the radius of the circle is

• A. $2$ units
• B. $\pi$ units
• C. $4$ units
• D. $7$ units

Answer 1

The correct option is A

$2$ units

Find the radius of the circle

Let $r$ be the radius of a circle.

We know that, Area of the circle = $\pi r^2$

Perimeter of the circle = $2\pi r$

Given that the perimeter and the area of a circle are numerically equal.

$$\begin{gathered} \Rightarrow \pi r^2=2\pi r \\ \Rightarrow r^2=2r \\ \Rightarrow r=2 \end{gathered}$$

Hence, the radius of the circle is $2$ units, so, option (A) is the correct answer.