Question

Campbells wants to try and sell their soup in boxes rather than cans. The originalcans have a height of 6 inches and a diameter of 4 inches. If the boxes can only be 2inches deep, 4 inches wide and the keep the volume the same, what is the height ofthe new rectangplar box?

Answer 1

Given

Original cans

Height of 6 inches

Diameter of 4 inches

New boxes

2 inches deep

4 inches wide

Same volume

Procedure

Now let's calculate the volume of the soup cans.

`\begin{gathered} V=\pi r^2h \\ V=\pi(2)^2(6) \\ V=75.36\text{ cubic inches} \end{gathered}`

Now let's calculate the volume of the boxes

`\begin{gathered} V=2\cdot4\cdot h \\ V=8h \end{gathered}`

Now we must equal the volume of the cans and then calculate the height.

`\begin{gathered} 75.36=8h \\ h=(75.36)/(8) \\ h=9.42\text{ inches} \end{gathered}`

The height of the boxes must be equal to 9.42 inches.