Final answer:
The height of the stack of blocks is the sum of the side lengths of each block, which are the cube roots of their volumes. Upon calculation, the total height of the stack is approximately 25.97 inches, which doesn't match any of the provided options.
Step-by-step explanation:
To find the height of a stack of cube-shaped blocks, we need to determine the height of each individual cube and then add them together. Since the volume of a cube is given by the formula volume = length x width x height, and in a cube, all sides are equal, we can say that the volume equals side length cubed. Therefore, to find the side length of each cube, we take the cube root of the volume.
- For the first block: side length = ∛375 = 7.21 inches (approx).
- For the second block: side length = ∛648 = 8.66 inches (approx).
- For the third block: side length = ∛1029 = 10.10 inches (approx).
Adding these side lengths together gives us the total height of the stack: 7.21 + 8.66 + 10.10 = 25.97 inches. None of the given options A, B, C, or D match the calculated height. Therefore, we may conclude that there might have been an error in the question, or more information is needed to select the correct option.