Answer:
56 inches (perimeter) * 14 inches (height) = 784 inches
Explanation:
To find the length of the wire used to form the framework of a cube, we need to consider the perimeter of the cube's base and multiply it by the height of the cube.
The volume of the cube is given as 2744 cubic inches. Since the volume of a cube is calculated by multiplying the length, width, and height of the cube, we can find the length of each side of the cube by taking the cube root of the volume.
∛2744 = 14
So, each side of the cube measures 14 inches.
To find the perimeter of the cube's base, we multiply the length of one side by 4 (since the base of a cube has 4 sides of equal length).
14 inches * 4 = 56 inches
Therefore, the perimeter of the cube's base is 56 inches.
To find the length of the wire used to form the framework of the cube, we multiply the perimeter of the base by the height of the cube. Since all sides of a cube are equal, the height is also equal to the length of one side, which is 14 inches.
56 inches (perimeter) * 14 inches (height) = 784 inches
So, the length of the wire used to form the framework of the cube is 784 inches.