Question

a box is 8 feet long, 2 feet wide, and 2 feet tall. what is the relationship between the volume of this box and the one in problem 3? tell how you know.

Explanation:

Step1: Recall volume formula

The volume formula for a rectangular - box (a rectangular prism) is $V = l\times w\times h$, where $l$ is the length, $w$ is the width, and $h$ is the height.

Step2: Substitute given values

Given $l = 8$ feet, $w = 2$ feet, and $h = 2$ feet. Substitute into the formula: $V=8\times2\times2$.

Step3: Calculate the volume

$V = 8\times2\times2=32$ cubic feet. But we don't know the volume of the box in problem 3, so we can't directly state the relationship between the volumes. However, if we assume the box in problem 3 has length $l_3$, width $w_3$, and height $h_3$, its volume $V_3=l_3\times w_3\times h_3$. The relationship between the volumes of the two boxes is $\frac{V}{V_3}=\frac{8\times2\times2}{l_3\times w_3\times h_3}$.

Answer:

The volume of the given box is 32 cubic feet. The relationship between the volume of this box and the box in problem 3 is $\frac{32}{V_3}$, where $V_3$ is the volume of the box in problem 3.