The volume of the rectangular prism is 36 ft³.
Step-by-step explanation:
Step 1:
The volume of a rectangular prism
,
The area of the base is length multiplied by the width. So ![Area = (l)(w).](https://tex.z-dn.net/?f=Area%20%3D%20%28l%29%28w%29.)
The volume of a rectangular prism = ![(area)(h).](https://tex.z-dn.net/?f=%28area%29%28h%29.)
The volume of a rectangular pyramid![= a^{2} \frac{h}{3} .](https://tex.z-dn.net/?f=%3D%20a%5E%7B2%7D%20%5Cfrac%7Bh%7D%7B3%7D%20.)
Where a is the side length. If the base is a square, the area
.
So the volume of a rectangular pyramid
.
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 = ![(12)(3) = 36.](https://tex.z-dn.net/?f=%2812%29%283%29%20%3D%2036.)
The volume of the rectangular prism is 36 ft³.