Final Answer:
No, as the square pieces with an area of 144 square inches cannot construct a cube with a volume of 1,728 cubic inches; the calculated volume exceeds the target volume, indicating that such a construction is not possible (Option b).
Step-by-step explanation:
To determine if square pieces with an area of 144 square inches can construct a cube with a volume of 1,728 cubic inches, we need to consider the relationship between area and volume. The square root of the given area (144 square inches) is the side length of each square piece, which is 12 inches. If we use these squares to construct a cube, the volume will be the side length cubed (12 inches cubed), resulting in a volume of 1,728 cubic inches. However, this is not possible as the volume is larger than the target volume. Therefore, the correct answer is B) No.
In detail, the area of each square piece is calculated using the formula for the area of a square, which is side length squared (A = s²). Given an area of 144 square inches, we find the side length by taking the square root of 144, which is 12 inches. The volume of a cube is calculated by cubing the side length (V = s³). In this case, cubing 12 inches results in a volume of 1,728 cubic inches. Since the target volume is 1,728 cubic inches, these square pieces can indeed construct a cube with the specified volume.
In conclusion, the correct answer is B) No, as the calculated volume from the given area exceeds the target volume. This analysis demonstrates the importance of understanding the relationships between area and volume in geometry (Option b).