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

$\begin{gathered} w=\frac{20}{5} \\ w=4 \end{gathered}$

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