Question

tavin is building flower boxes in the shape of a rectangular prism. the first box has a length of 10 feet, a width of 2 feet and an unknown height. the second box has a length of 5 feet and the same height as the first box.if the two volumes are to be the same what should the width of the second box be?

Answer 1

The volume of a rectangular prism can be obtained using the formula

`V=l\cdot w\cdot h`

the volume for the first box is

`\begin{gathered} V=10\cdot2\cdot h \\ V=20h \end{gathered}`

the volume for the second box is

`V=5\cdot w\cdot h`

if both volumes are equal then both expressions can be equaled

`20\cdot h=5\cdot w\cdot h`

since both boxes have the same height, then h is equal on both sides and can be cancelled out.

`20=5w`

solve the expression for w

`\begin{gathered} w=(20)/(5) \\ w=4 \end{gathered}`

the width of the second box should be 4 feet in order for them to have the same volume.