Let's break this problem into manageable steps:
1. Total Volume of the Column: We are given that the total volume of the column is 15 cubic inches.
2. Number of Crackers: We are also informed that there are 40 crackers in this column.
3. Volume Definition: The volume of a rectangular prism (which each cracker is) can be defined as:
[tex]\[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}
\][/tex]
4. Height Calculation: To find the height of each cracker, we need to determine how much volume one cracker takes up. Since the total volume for 40 crackers is 15 cubic inches, the volume of one cracker is:
[tex]\[
\text{Volume of one cracker} = \frac{\text{Total Volume}}{\text{Number of Crackers}} = \frac{15 \text{ cubic inches}}{40} = 0.375 \text{ cubic inches}
\][/tex]
5. Known Dimensions: Each cracker measures 2 inches in length and [tex]\(1 \frac{1}{2}\)[/tex] inches in width. Converting [tex]\(1 \frac{1}{2}\)[/tex] inches to an improper fraction or a decimal gives us 1.5 inches.
6. Height of Each Cracker: Given that:
[tex]\[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}
\][/tex]
Substituting the known dimensions:
[tex]\[
0.375 = 2 \text{ inches} \times 1.5 \text{ inches} \times \text{Height}
\][/tex]
7. Solve for Height:
[tex]\[
0.375 = 3 \times \text{Height}
\][/tex]
[tex]\[
\text{Height} = \frac{0.375}{3} = 0.125 \text{ inches}
\][/tex]
8. Convert to Fraction: Finally, 0.125 inches is equivalent to:
[tex]\[
0.125 = \frac{1}{8} \text{ inches}
\][/tex]
Therefore, the height of each individual cracker is [tex]\( \frac{1}{8} \)[/tex] inch. The final answer is:
[tex]\(\boxed{\frac{1}{8}}\)[/tex]
