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.

Respuesta :

When the window is expanded to be 4 feet high by 4 feet wide, the volume of the wall quadruples or increases by factor of 4.

Volume of the wall

The volume of the wall is determined as follows;

V = h x w x t

where;

  • t is the thickness of the wall
  • h is height of the wall
  • w is width of the wall

Initial volume of the wall when some blocks are removed to make a window is 2 feet high by 2 feet wide.

V1 = (6 - 2) x (6 - 2) x (t)

V1 = 16t  ft³

Second volume of the wall when some blocks are removed to make a window is 4 feet high by 4 feet wide.

V2 = (12 - 4) x (12 - 4) x (t)

V2 = 64t  ft³

V2 = 4(16t  ft³)

V2 = 4(V1)

Thus, when the window is expanded to be 4 feet high by 4 feet wide, the volume of the wall quadruples or increases by factor of 4.

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