Answer :
Given the problem, let's break down the solution step-by-step:
1. Volume of the Column:
- The total volume of the column of crackers is given as 15 cubic inches.
2. Number of Crackers:
- There are 40 crackers in the column.
3. Volume of Each Cracker:
- To find the volume of each cracker, divide the total volume of the column by the number of crackers:
[tex]\[ \text{Volume of each cracker} = \frac{\text{Total volume of column}}{\text{Number of crackers}} = \frac{15 \text{ in}^3}{40} = 0.375 \text{ cubic inches} \][/tex]
4. Dimensions of Each Cracker:
- The length of each cracker is 2 inches, and the width is \(1 \frac{1}{2}\) inches.
[tex]\[ \text{Length} = 2 \text{ inches}, \quad \text{Width} = 1.5 \text{ inches} \][/tex]
5. Height of Each Cracker:
- The volume of a rectangular prism (or cracker in this case) is calculated as:
[tex]\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \][/tex]
- Given that the volume of each cracker is 0.375 cubic inches, we can solve for the height \( h \):
[tex]\[ 0.375 = 2 \times 1.5 \times h \][/tex]
- Simplify the equation:
[tex]\[ 0.375 = 3 \times h \][/tex]
- Solve for \( h \):
[tex]\[ h = \frac{0.375}{3} = 0.125 \text{ inches} \][/tex]
6. Conclusion:
- The height of each cracker is 0.125 inches.
Thus, from the given multiple-choice options, the correct answer is:
[tex]\[ \frac{1}{8} \text{ inch} \][/tex]
Therefore, the height of each individual cracker is [tex]\( \frac{1}{8} \)[/tex] inch.
1. Volume of the Column:
- The total volume of the column of crackers is given as 15 cubic inches.
2. Number of Crackers:
- There are 40 crackers in the column.
3. Volume of Each Cracker:
- To find the volume of each cracker, divide the total volume of the column by the number of crackers:
[tex]\[ \text{Volume of each cracker} = \frac{\text{Total volume of column}}{\text{Number of crackers}} = \frac{15 \text{ in}^3}{40} = 0.375 \text{ cubic inches} \][/tex]
4. Dimensions of Each Cracker:
- The length of each cracker is 2 inches, and the width is \(1 \frac{1}{2}\) inches.
[tex]\[ \text{Length} = 2 \text{ inches}, \quad \text{Width} = 1.5 \text{ inches} \][/tex]
5. Height of Each Cracker:
- The volume of a rectangular prism (or cracker in this case) is calculated as:
[tex]\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \][/tex]
- Given that the volume of each cracker is 0.375 cubic inches, we can solve for the height \( h \):
[tex]\[ 0.375 = 2 \times 1.5 \times h \][/tex]
- Simplify the equation:
[tex]\[ 0.375 = 3 \times h \][/tex]
- Solve for \( h \):
[tex]\[ h = \frac{0.375}{3} = 0.125 \text{ inches} \][/tex]
6. Conclusion:
- The height of each cracker is 0.125 inches.
Thus, from the given multiple-choice options, the correct answer is:
[tex]\[ \frac{1}{8} \text{ inch} \][/tex]
Therefore, the height of each individual cracker is [tex]\( \frac{1}{8} \)[/tex] inch.
