Question

a company makes japanese - style lunch boxes called bento boxes. each bento box is a cube with $\frac{1}{2}$ - foot - long edges. the company ships the bento boxes in a container in the shape of a rectangular prism that measures $\frac{7}{2}$ feet by $\frac{3}{2}$ feet by $\frac{3}{2}$ feet. a manager correctly finds the volume of the container using a formula. an employee double - checks the calculation by packing the container full of bento boxes. use the drop - down menus to explain how both volume calculations compare. click the arrows to choose an answer from each menu. the manager can find the volume of the container using the formula choose... the employee correctly determines that the container can be filled with choose... bento boxes. he can find the volume of the container by multiplying the number of bento boxes that fill the container by the choose... of one bento box. the volume found by using the formula is choose... the volume of the total number of bento boxes in the container.

Explanation:

Step1: Recall volume formula for rectangular prism

The volume formula for a rectangular prism is $V = l\times w\times h$, where $l$ is the length, $w$ is the width and $h$ is the height. So the manager can find the volume of the container using the formula $V=\frac{7}{2}\times\frac{3}{2}\times\frac{3}{2}$.

Step2: Find volume of one bento - box

The volume of a cube (bento - box) with side length $s$ is $V_{b}=s^{3}$. Since $s = \frac{1}{2}$ foot, $V_{b}=(\frac{1}{2})^{3}=\frac{1}{8}$ cubic feet.

Step3: Find number of bento - boxes in the container

The number of bento - boxes along the length $n_{l}=\frac{\frac{7}{2}}{\frac{1}{2}} = 7$, along the width $n_{w}=\frac{\frac{3}{2}}{\frac{1}{2}}=3$, and along the height $n_{h}=\frac{\frac{3}{2}}{\frac{1}{2}} = 3$. The total number of bento - boxes $n=n_{l}\times n_{w}\times n_{h}=7\times3\times3 = 63$.

Step4: Compare the two volume calculations

The volume of the container found by multiplying the number of bento - boxes by the volume of one bento - box is $V=n\times V_{b}=63\times\frac{1}{8}=\frac{7}{2}\times\frac{3}{2}\times\frac{3}{2}$. So the volume found by using the formula is equal to the volume of the total number of bento - boxes in the container.

Answer:

The manager can find the volume of the container using the formula $V = l\times w\times h$ (where $l=\frac{7}{2}$, $w = \frac{3}{2}$, $h=\frac{3}{2}$).
The employee correctly determines that the container can be filled with 63 bento - boxes. He can find the volume of the container by multiplying the number of bento - boxes that fill the container by the volume of one bento - box.
The volume found by using the formula is equal to the volume of the total number of bento - boxes in the container.