Question

a type of cracker, rectangular in shape, is stored in a vertical column with all of the crackers stacked directly on top of each other. each cracker measures 2 inches in length by $1\frac{1}{2}$ inches in width. the volume of the column is 15 inches cubed. if there are 40 crackers in the column, what is the height of each individual cracker? $\frac{3}{40}$ inch $\frac{1}{8}$ inch $\frac{1}{5}$ inch $\frac{3}{8}$ inch

Explanation:

Step1: Define total height variable

Let $H$ = total height of the column, $h$ = height of 1 cracker.

Step2: Calculate base area of column

Base area = length $\times$ width = $2 \times 1\frac{1}{2} = 2 \times \frac{3}{2} = 3$ square inches

Step3: Relate volume to total height

Volume = base area $\times$ total height, so $15 = 3 \times H$
Solve for $H$: $H = \frac{15}{3} = 5$ inches

Step4: Find height of 1 cracker

Total height = 40 $\times$ individual height, so $5 = 40h$
Solve for $h$: $h = \frac{5}{40} = \frac{1}{8}$ inches

Answer:

$\frac{1}{8}$ inch