SOLUTION: The problem says "A cylindrical tank has a volume of 300 gallons. A similar tank next to it has dimensions that are 3 times as large. What is the volume of the larger tank?"
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Question 542532: The problem says "A cylindrical tank has a volume of 300 gallons. A similar tank next to it has dimensions that are 3 times as large. What is the volume of the larger tank?"
I was thinking that you would multiply the volume of the first tank by 3. But then again i'm not that sure! Please help!
Found 2 solutions by Alan3354, Theo:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
The problem says "A cylindrical tank has a volume of 300 gallons. A similar tank next to it has dimensions that are 3 times as large. What is the volume of the larger tank?"
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If both the radius and height are 3 times, the volume is 27 times.
gallons
gallons
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i would think this means that the larger tank is 3 times as high and 3 times as wide.
if we assume that the smaller tank has a height of h and a diameter of 2r, then the larger tank would have a height of 3h and a diameter of 6r.
the volume of the smaller tank is equal to:
pi * r^2 * h
h is the height
r is the radius
the radius is equal to 1/2 the length of the diameter.
the volume of the larger tank would therefore be equal to:
pi * (3 * r)^2 * (3 * h)
this becomes:
pi * 3^2 * r^2 * 3 * h which becomes:
pi * 9 * r^2 * 3 * h which becomes:
pi * 27 * r^2 * h
based on this, the volume of the larger tank should be 27 times larger than the volume of the smaller tank.
volume of the smaller tank is pi * r^2 * h
volume of the larger tank is pi * 27 * 4^2 * h
divide the volume of the larger tank by the volume of the smaller tank and you get a ratio of 27 / 1 which is equal to 27.
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