SOLUTION: Charlie built a treasure box. Lucy build a treasure box with dimensions twice as large as Charlie's. If it takes one-half gallon of paint to vover the surface of Charlie's box, how

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Let , , and be the length width and height of Charlie's box.

So the volume of Charlie's box is


Also, the surface area of Charlie's box is




Factor out the GCF 2.

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Now let , , and be the length width and height of Lucy's box.


Since Lucy's box has " dimensions twice as large as Charlie's", this means that , , and



So the volume of Lucy's box is



Now plug in , , and


Multiply


So the volume of Lucy's box is 8 times larger than Charlie's box.




Also, the surface area of Lucy's box is




Factor out the GCF 2.

Now plug in , , and


Multiply


Factor out the GCF 4 and multiply it by the outer term 2


So the surface area of Lucy's box is 8 times the surface area of Charlie's box. So she needs 8 times more paint than Charlie.


So simply multiply the amount of paint that Charlie uses (one half gallons) by 8 to get



So she needs 4 gallons of paint to cover her box.