In the diagram, square $W X Y Z$ has area 9 and $W$ is at the centre of a circle. If $X$ and $Z$ are on the circle, the area of the circle is
(A) $3 \pi$
(B) $6 \pi$
(C) $9 \pi$
(D) $18 \pi$
(E) $81 \pi$

![](https://cdn.mathpix.com/cropped/2024_04_20_ac36362783317e0251fdg-056.jpg?height=452&width=336&top_left_y=1216&top_left_x=1293)
Since square $W X Y Z$ has area 9 , then its side length is $\sqrt{9}=3$.

Since $W$ is the centre of the circle and $X$ lies on the circumference of the circle, then $W X$ is a radius of the circle, so the radius of the circle has length 3 .

Therefore, the area of the circle is $\pi\left(3^{2}\right)=9 \pi$.

ANSWER: (C)