The volume of the rectangular prism is 36 ft³.
Step-by-step explanation:
Step 1:
The volume of a rectangular prism [tex]= lwh[/tex],
The area of the base is length multiplied by the width. So [tex]Area = (l)(w).[/tex]
The volume of a rectangular prism = [tex](area)(h).[/tex]
The volume of a rectangular pyramid[tex]= a^{2} \frac{h}{3} .[/tex]
Where a is the side length. If the base is a square, the area [tex]= a^{2}[/tex].
So the volume of a rectangular pyramid[tex]=\frac{1}{3} (area)(h)[/tex].
So if a rectangular pyramid and a rectangular prism have the same base and height, then
3 times the volume of the rectangular pyramid = The volume of the rectangular prism.
Step 2:
As it is given that the volume of the pyramid is 12 ft³, we can calculate the volume of the prism. As both the shapes have the same height and base,
The volume of the prism = [tex](12)(3) = 36.[/tex]
The volume of the rectangular prism is 36 ft³.
