Question : If the numerical value of the circumference and area of a circle is the same, then the area is:
Option 1: $6\pi$ sq. units
Option 2: $4\pi$ sq. units
Option 3: $8\pi$ sq. units
Option 4: $12\pi$ sq. units
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Correct Answer: $4\pi$ sq. units
Solution :
Given: the numerical value of the circumference and area of a circle is the same.
Let the radius of the circle be $r$ unit.
We know that, the circumference of a circle = $2\pi r$,
and the area of a circle = $\pi r^2$
According to the question,
$\pi r^2$ = $2\pi r$
⇒ $r$ = $2$ units
Therefore, the area of the circle = $\pi r^2$ = $\pi(2)^2$ = $4\pi$ sq.units
Hence, the correct answer is $4\pi$ sq. units.
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