The area (in sq. units) of the region enclosed by the circle \(x^{2}+y^{2}=2\) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(2\pi\)
The circle \(x^{2}+y^{2}=r^{2}\) has centre at the origin and radius r, and it encloses an area \(\pi r^{2}\).
Here
\(r^{2} = 2\)
So the area is
\(A = \pi r^{2} = 2\pi\)
Why the other options are incorrect
Option (1) \(4\pi\) — Incorrect. This takes the radius as 2; the radius is \(\sqrt{2}\), since \(r^{2} = 2\).
Option (3) \(\sqrt{2}\,\pi\) — Incorrect. This is \(\pi r\), not \(\pi r^{2}\).
Option (4) \(\pi\) — Incorrect. This is the area of a circle of radius 1.