The volume of a rectangular pyramid can be found using the formula V = (1/3)AH 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)AH
V' = (1/3)(3A)(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)AH]/[
A(H/7)] = 7/3
(3/7)V = V'
So, the volume of the new pyramid is 3/7 times the old one.
