Final answer:
To find the height of the rectangular prism with a given volume of 473.2 cubic millimeters, length of 7 millimeters, and width of 10.4 millimeters, use the formula h = V / (lw). The height is calculated to be approximately 6.5 millimeters.
Step-by-step explanation:
The volume of a rectangular prism is calculated by multiplying its length (l), width (w), and height (h) together. The formula is V = lwh, where V is volume. To find the height when you know the other dimensions and the volume, you rearrange this formula to solve for the height: h = V / (lw).
In this case, the volume (V) is 473.2 cubic millimeters, the length (l) is 7 millimeters, and the width (w) is 10.4 millimeters. Plug these numbers into the formula to find the height: h = 473.2 mm³ / (7 mm * 10.4 mm).
Performing the calculation, you get h = 473.2 mm³ / 72.8 mm², which simplifies to approximately h = 6.5 mm. Therefore, the height of the rectangular prism is 6.5 millimeters.