Solution
- The formula for finding the volume of the prism is:
[tex]\begin{gathered} V=l\times w\times 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\times h \\ where, \\ l=w=x \end{gathered}[/tex]- We have been given the height to be 9ft. Thus, we can find the length of a side by applying the formula:
[tex]\begin{gathered} V=9x^2 \\ V=441 \\ \\ \therefore441=9x^2 \\ \text{ Divide both sides by 9} \\ x^2=\frac{441}{9} \\ \\ \text{ Take the square root of both sides} \\ x=\sqrt{\frac{441}{9}} \\ \\ x=\frac{21}{3}=7 \end{gathered}[/tex]Final Answer
The length of a side of the base is x = 7.
