To find the constant of proportionality, we need to divide the height of the stack by the number of cases.
In this case, we have:
- Height of the stack (for 8 cases) = 120 mm
- Number of cases = 8
The constant of proportionality (k) can be calculated as follows:
\[ k = \frac{\text{Height}}{\text{Number of cases}} = \frac{120 \text{ mm}}{8 \text{ cases}} = 15 \text{ mm per case} \]
Now, to find the height of a stack of 14 cases using the constant of proportionality:
\[ \text{Height for 14 cases} = k \times \text{Number of cases} = 15 \text{ mm per case} \times 14 \text{ cases} = 210 \text{ mm} \]
In summary:
- The constant of proportionality is 15 mm per DVD case.
- The height of a stack of 14 cases is 210 mm.