SOLUTION: a can has a height H and a radius R the total surface area is 4 times more than that of another can which is smaller withthe same radius R but height h PROVE that R=H-4h /2

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Question 258742: a can has a height H and a radius R the total surface area is 4 times more than that of another can which is smaller withthe same radius R but height h
PROVE that R=H-4h /2
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Surface area for the can is the sum of the circular top and bottom and the rolled out portion of the side, which rolls out to a rectangle.
SA1=pi%2AR%5E2%2Bpi%2AR%5E2%2B2%2Api%2AR%2AH=2%2Api%2A%28R%5E2%2BR%2AH%29
SA2=pi%2AR%5E2%2Bpi%2AR%5E2%2B2%2Api%2AR%2Ah=2%2Api%2A%28R%5E2%2BR%2Ah%29
You also know that
SA1=4%2ASA2
2%2Api%2A%28R%5E2%2BR%2AH%29=8%2Api%2A%28R%5E2%2BR%2Ah%29
R%5E2%2BR%2AH=4R%5E2%2B4%28R%2Ah%29%29
R%2AH=3R%5E2%2B4%28R%2Ah%29%29
H-4%2Ah=3R
R=%281%2F3%29%28H-4%2Ah%29
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I don't get the same answer. Are you sure it's a 2 dividing the entire height term on the right hand side??