Question

A right rectangular prism has a volume of 30 cubic inches. it's length is 1/3 -inch and its width is 36in. what is the height? include units of measure in your response.

Answer 1

The formula of the volume of a right rectangular prism is:

`V=\text{width}* height* length`

Given the formula above, we can derive the formula for the height and that is:

`\begin{gathered} V=whl \\ (V)/(wl)=(whl)/(wl) \\ (V)/(wl)=h \end{gathered}`

Since we know that Volume = 30 in³, length = 1/3 in, and width is 36 in, let's plug this in to the formula above for height.

`\begin{gathered} h=(V)/(wl) \\ h=(30in^3)/((36in)((1)/(3)in)) \\ h=(30in^3)/(12in^2) \\ h=2.5in \end{gathered}`

Answer: Therefore, the height of the prism is 5/2 or 2.5 inches.