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 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?

1. 3/40 inch
2. 1/8 inch
3. 1/3 inch
4. 3/8 inch

Explanation:

Step1: Calculate volume of 1 cracker

The volume of the column of 40 crackers is 15 cubic - inches. So the volume of 1 cracker $V_1=\frac{15}{40}=\frac{3}{8}$ cubic - inches.

Step2: Use volume formula for rectangular - shaped cracker

The volume formula for a rectangular solid is $V = l\times w\times h$, where $l = 2$ inches, $w = 1\frac{1}{2}=\frac{3}{2}$ inches, and $h$ is the height we want to find. We know $V=\frac{3}{8}$ cubic - inches, $l = 2$ inches, and $w=\frac{3}{2}$ inches. Substituting into the formula $\frac{3}{8}=2\times\frac{3}{2}\times h$.

Step3: Solve for height $h$

First, simplify the right - hand side of the equation: $2\times\frac{3}{2}=3$. So the equation becomes $\frac{3}{8}=3h$. Then solve for $h$ by dividing both sides of the equation by 3: $h=\frac{3}{8}\div3=\frac{3}{8}\times\frac{1}{3}=\frac{1}{8}$ inches.

Answer:

$\frac{1}{8}$ inch