Question

the volume of a rectangular prism 9ft long with a square face is described as V= 9x2. What is the length of a side on the square face (x=?) if the volume = 441 ft3

Answer 1

- The formula for finding the volume of the prism is:

`\begin{gathered} V=l* w* h \\ where, \\ l=length \\ w=width \\ h=height \\ \\ \text{ But we have been told that the base is a square. In a square the width and length} \\ \text{ are equal. Thus, the volume is:} \\ \\ V=x^2* h \\ where, \\ l=w=x \end{gathered}`

- We have been given the height to be 9ft. Thus, we can find the length of a side by applying the formula:

`\begin{gathered} V=9x^2 \\ V=441 \\ \\ \therefore441=9x^2 \\ \text{ Divide both sides by 9} \\ x^2=(441)/(9) \\ \\ \text{ Take the square root of both sides} \\ x=\sqrt{(441)/(9)} \\ \\ x=(21)/(3)=7 \end{gathered}`

Final Answer

The length of a side of the base is x = 7.