For this case we have that by definition, the volume of a rectangular prism is given by:
[tex]V = A_ {b} * h[/tex]
Where:
[tex]A_ {b}:[/tex]It is the area of the base of the prism
h: It is the height
[tex]A_ {b} = w * l[/tex]
Where:
w: is the width
l: is the length
According to the data of the statement we have:
[tex]w = 16 \ in\\l = 4h\\V = 4,096 \ in ^ 3[/tex]
Substituting the data we have:
[tex]A_ {b} = 16 * 4h = 64h\\64h * h = 4,096\\64h ^ 2 = 4,096\\h ^ 2 = \frac {4096} {64}\\h ^ 2 = 64\\h = \pm \sqrt {64}\\[/tex]
We choose the positive value: [tex]h = 8[/tex]
So the height is[tex]8 \ in[/tex]
Answer:
[tex]8 \ in[/tex]
