Lauren’s family room is the shape of a rectangular prism with a volume of 1,120 cubic feet. If she decides to knock out the wall and triple the length of her family room, what will happen to the volume?

Let a be the width of Lauren’s family room, b be the length of it and c - the height. Then the volume of Lauren’s family room is a volume of a rectangular prism:

[tex]V=a\cdot b\cdot c.[/tex]

This volume is equal to 1,120 cubic feet, so [tex]abc=1,120.[/tex]

If she triples the length of her family room, then new length is 3b (width and height left the same) and new volume is

[tex]V_{new}=a\cdot 3b\cdot c=3abc=3V=3\cdot 1,120=3,360[/tex] cubic feet.

Answer: the new volume will be tripled and its value will be 3,360 cubic feet.