A rectangular pyramid and a rectangular prism are shown below.

If the volume of the pyramid is 12 ft3, what is the volume of the prism? Explain why and how you found your answer.

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

The volume of a rectangular prism =

The volume of a rectangular pyramid

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 =

The volume of the rectangular prism is 36 ft³.

you forgot an image

step-by-step explanation:

step-by-step explanation :

we know that

the measurement of the outer angle is the semi-difference of the arcs which comprises

in this problem

m< xzy is the outer angle

substitute the values

the measure of angle xoy is equal to

> by central angle

substitute the value