Question

Three rectangular prisms each have a volume of 60 cubic inches. Complete the table to show the length, width, and height of each rectangular prism. Rectangular Prism Length (in) Width (in) Height (in) A inches 2 inches 5 inches 5 inches inghes 4 inches

Answer 1

The volume of a rectangular prism is the product of its 3 dimensions: length, width and height.

Then, the product of the three dimensions has to be equal to 60 cubic inches for the 3 prisms.

All the units are in inches, so we don't have to do any conversion.

Rectangular Prism A

`\begin{gathered} V=L\cdot W\cdot H=L\cdot2\cdot5=60 \\ L\cdot10=60 \\ L=(60)/(10) \\ L=6\text{ in} \end{gathered}`

The length of A is 6 inches.

Rectangular Prism B

`\begin{gathered} V=L\cdot W\cdot H \\ V=5\cdot W\cdot4=60 \\ W\cdot20=60 \\ W=(60)/(20) \\ W=3\text{ in} \end{gathered}`

The width of B is 3 inches.

Rectangular Prism C

`\begin{gathered} V=L\cdot W\cdot H \\ V=10\cdot2\cdot H=60 \\ 20\cdot H=60 \\ H=(60)/(20) \\ H=3\text{ in} \end{gathered}`

The height of C is 3 inches.