Final answer:
To find the area of the square ABCD inscribed with circle Q, we need to determine the length of its side. First, calculate the radius of the circle using the formula A = πr^2. Then, find the side length of the square, which is twice the radius. Finally, calculate the area of the square using the formula A = s^2.
Step-by-step explanation:
To find the area of the square ABCD, we need to determine the length of its side. Since the circle Q is inscribed in the square, the diameter of the circle is equal to the side length of the square. Let's find the radius of the circle first. The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.
Given that the area of circle Q is 350 cm², we can use the formula to solve for the radius: 350 = πr^2. Dividing both sides of the equation by π gives us r^2 = 350/π. Taking the square root of both sides, we get r ≈ √(350/π).
Now that we have the radius, the side length of the square is 2r. We can calculate the area of the square using the formula A = s^2, where A is the area and s is the side length. Substituting in the value for s, we get A ≈ (2r)^2 = 4r^2.
Replacing r with its approximate value, we have A ≈ 4(√(350/π))^2. Evaluating this expression will give us the area of the square ABCD to the nearest 0.1 cm².