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

Question 149518: 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 many gallons of paint would it take to paint Lucy's box? How many times more volume will Lucy's box hold than Charlie's?

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

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.

--------------------

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.

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