Final Answer:
36π square inches of cloth cut from the square.(C)
Step-by-step explanation:
To find the area of the cloth cut out in the shape of a circle from a square, we can use the formula for the area of a circle. The area of a circle is given by the formula A = πr², where r is the radius of the circle. In this case, the square's side length is also the diameter of the circle, so the radius is half of the side length.
The area of the square is found by squaring its side length. If the side length of the square is 's', then the area of the square is A = s². In this scenario, the square's area equals the area of the circle plus the remaining area of the square not occupied by the circle.
Given that the square's side length is 6 inches, the area of the square is 6² = 36 square inches. The radius of the circle (which is half of the side length) is 3 inches. Hence, the area of the circle is π * (3)² = 9π square inches. Subtracting the area of the circle from the area of the square gives us the remaining area, which is 36 - 9π = 27π square inches. This remaining area is the cloth cut out from the square, resulting in a total of 36π square inches of cloth cut from the square.
Therefore, the final answer is 36π square inches of cloth cut from the square, option C.