Question

A rectangular pyramid and a rectangular prism are shown below.

Answer 1

The volume of the rectangular prism is 36 ft³.

Step-by-step explanation:

Step 1:

The volume of a rectangular prism $= lwh$,

The area of the base is length multiplied by the width. So $Area = (l)(w).$

The volume of a rectangular prism = $(area)(h).$

The volume of a rectangular pyramid$= a^{2} \frac{h}{3} .$

Where a is the side length. If the base is a square, the area $= a^{2}$.

So the volume of a rectangular pyramid$=\frac{1}{3} (area)(h)$.

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 = $(12)(3) = 36.$

The volume of the rectangular prism is 36 ft³.