The length of the base of a rectangular pyramid is tripled, the width of the base remains the same, and the height of the pyramid is divided by 7. what volume formula reflects these changes?

The volume of a rectangular pyramid can be found using the formula V = (1/3)*A*H where A is the area of the rectangle base, and H is the height of the pyramid

The length of the base is tripled and the width of the base remains the same. Then, the new area of the base is 3 times the old one.

The height of the pyramid is divided by 7. Then, the new height is the old one divided by 7.

Replacing this in the formula:

V = (1/3)*A*H

V' = (1/3)*(3*A)*(H/7)

V' =   A*(H/7)

where V' is the volume of the new pyramid. Notice that, A and H refer to the original pyramid.

The relationship between these volumes are:

V/V' = [(1/3)*A*H]/[ A*(H/7)] = 7/3

(3/7)*V = V'

So, the volume of the new pyramid is 3/7 times the old one.