Question

The height of a pyramid is doubled, but its length and width are cut in half. What is true about the volume of the new pyramid?

A. The new pyramid has a volume that is a the volume of the original pyramid.
B. The new pyramid has a volume that is ż the volume of the original pyramid.
C. The new pyramid has the same volume as the volume of the original pyramid.
D. The new pyramid has a volume that is 2 times the volume of the original pyramid.

Answer 1

The new pyramid has a volume that is half the volume of the original pyramid.

Explanation:

The volume of a pyramid is given by the following equation:

`V = (h*l*w)/(3)`

In which h is the height, l is the length and w is the width.

Modified volume:

height doubled, length and width cut in half. So

`h = 2h, l = 0.5l, w = 0.5w`

`V_(M) = (2h*0.5l*0.5l)/(3) = (0.5*h*l*w)/(3) = 0.5(h*l*w)/(3)` = 0.5V[/tex]

That is

The new pyramid has a volume that is half the volume of the original pyramid.