A circle is inscribed in a square of side $\sqrt 6$. What is the area of the circle?
- $\displaystyle \frac{3}{2}\pi $
- 6$\displaystyle \pi $
- $\displaystyle \pi $
- 9$\displaystyle \pi $
Reveal answer
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A
Correct answer
Explanation
If a circle is inscribed in a square of side sqrt(6), the diameter of the circle is equal to the side of the square, so d = sqrt(6) and r = sqrt(6)/2. The area is pi * r^2 = pi * (6/4) = 1.5 * pi.
AI explanation
When a circle is inscribed in a square, its diameter equals the side length of the square, making the diameter the square root of 6. The radius is half of that, which is the square root of 6 divided by 2. The area of the circle is pi times the radius squared, so this becomes pi times the square of (the square root of 6 divided by 2). This simplifies to 6 divided by 4, resulting in 3 divided by 2 times pi.