Q. If the perimeter and the area of a circle are numerically equal, then the radius of the circle is
a) 7 unit
b) 2 unit
c) 4 unit
d) π unit
Correct Answer: b) 2 unit
Question from UPPSC Prelims CSAT 2025
Explanation:
Perimeter (circumference) of a circle = 2πr; Area of a circle = πr^2.
If they are numerically equal: 2πr = πr^2.
Dividing both sides by π gives 2r = r^2. Rearranging: r^2 − 2r = 0 ⇒ r(r − 2) = 0. Thus r = 0 or r = 2.
Radius cannot be zero for a non-degenerate circle, so r = 2 units.
Therefore, option 2 is correct.
