Question

A wall of a building is made from blocks that are each 1 cubic foot. The wall is 6 feet high and 6 feet wide. A window is made by removing some blocks as shown below. The window is 2 feet high by 2 feet wide.

The wall is 6 feet high and 6 feet wide. The window is 2 feet high by 2 feet wide and is cut from the center of the wall.

Suppose the wall is expanded to be 12 feet high by 12 feet wide, and the window is expanded to be 4 feet high by 4 feet wide. How will this change the volume of the wall?

A.
The volume will not change.

B.
The volume of the wall will double.

C.
The volume of the wall will increase by 96 cubic feet.

D.
The volume of the wall will increase by 128 cubic feet.

Answer 1

A. The volume will not change. The expansion of the wall and window is proportional, so the ratio of wall volume to window volume remains the same. Therefore, the added volume from expanding the wall is exactly balanced by the volume removed in expanding the window.