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

Algebra ->  Formulas -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!

Let L%5Bc%5D, W%5Bc%5D, and H%5Bc%5D be the length width and height of Charlie's box.

So the volume of Charlie's box is
V=L%5Bc%5D%2AW%5Bc%5D%2AH%5Bc%5D

Also, the surface area of Charlie's box is

SA=2%2AL%5Bc%5D%2AW%5Bc%5D%2B2%2AL%5Bc%5D%2AH%5Bc%5D%2B2%2AW%5Bc%5D%2AH%5Bc%5D


SA=2%28L%5Bc%5D%2AW%5Bc%5D%2BL%5Bc%5D%2AH%5Bc%5D%2BW%5Bc%5D%2AH%5Bc%5D%29 Factor out the GCF 2.

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Now let L%5Bl%5D, W%5Bl%5D, and H%5Bl%5D 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 L%5Bl%5D=2L%5Bc%5D, W%5Bl%5D=2W%5Bc%5D, and H%5Bl%5D=2H%5Bc%5D



So the volume of Lucy's box is
V=L%5Bl%5D%2AW%5Bl%5D%2AH%5Bl%5D


V=2L%5Bc%5D%2A2W%5Bc%5D%2A2H%5Bc%5D Now plug in L%5Bl%5D=2L%5Bc%5D, W%5Bl%5D=2W%5Bc%5D, and H%5Bl%5D=2H%5Bc%5D


V=8L%5Bc%5D%2AW%5Bc%5D%2AH%5Bc%5D 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

SA=2%2AL%5Bl%5D%2AW%5Bl%5D%2B2%2AL%5Bl%5D%2AH%5Bl%5D%2B2%2AW%5Bl%5D%2AH%5Bl%5D


SA=2%28L%5Bl%5D%2AW%5Bl%5D%2BL%5Bl%5D%2AH%5Bl%5D%2BW%5Bl%5D%2AH%5Bl%5D%29 Factor out the GCF 2.

SA=2%282L%5Bc%5D%2A2W%5Bc%5D%2B2L%5Bc%5D%2A2H%5Bc%5D%2B2W%5Bc%5D%2A2H%5Bc%5D%29 Now plug in L%5Bl%5D=2L%5Bc%5D, W%5Bl%5D=2W%5Bc%5D, and H%5Bl%5D=2H%5Bc%5D


SA=2%284L%5Bc%5D%2AW%5Bc%5D%2B4L%5Bc%5D%2AH%5Bc%5D%2B4W%5Bc%5D%2AH%5Bc%5D%29 Multiply


SA=8%28L%5Bc%5D%2AW%5Bc%5D%2BL%5Bc%5D%2AH%5Bc%5D%2BW%5Bc%5D%2AH%5Bc%5D%29 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

8%281%2F2%29=8%2F2=4

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