Answer :
Given the word problem, we can deduce the following information:
Volume of a rectangular pyramid=64 units^3
length of the rectangular base = 4 units
width of the rectangular base = 6 units
To determine the height of the pyramid, we use the formula as shown below:
[tex]h=3\frac{V}{lw}[/tex]where:
V= Volume of the rectangular pyramid
l=length of the rectangular base
w=width of the rectangular base
h=height of the pyramid
We plug in what we know:
[tex]\begin{gathered} h=3\frac{V}{lw} \\ =3\frac{64}{(4)(6)} \\ \text{Simplify} \\ =\frac{192}{24} \\ h=8\text{ units} \end{gathered}[/tex]Therefore, the height of the pyramid is 8 units.