133k views
2 votes
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?
O The new pyramid has a volume that is the volume of the original pyramid.
1
O The new pyramid has a volume that is the volume of the original pyramid.
O The new pyramid has the same volume as the volume of the original pyramia
O The new pyramid has a volume that is 2 times the volume of the original pyramid.

1 Answer

6 votes
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.
User Oleh Zayats
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories