The volume of a pyramid is given by the formula V = (1/3)Bh, where B is the area of the base and h is the height. If we double the height and cut the length and width in half, the new dimensions of the pyramid will be:
New height = 2h
New length = 0.5l
New width = 0.5w
The new volume of the pyramid can be calculated as follows:
New volume = (1/3)B(2h) = (2/3)Bh
The area of the new base, B, is given by:
B = (0.5l)(0.5w) = 0.25lw
Therefore, the new volume of the pyramid can be written as:
New volume = (2/3)(0.25lw)(2h) = (1/3)lwh
This is exactly half of the original volume of the pyramid, which means that the statement "The new pyramid has a volume that is 2 times the volume of the original pyramid" is false.
The correct answer is:
O The new pyramid has a volume that is the volume of the original pyramid.