Help with a volume expansion problem

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The problem involves calculating the volume of gasoline that spills from a 3.00-liter aluminum cylinder when heated from 5.00°C to 53.0°C, considering both the expansion of the aluminum container and the gasoline. The coefficients of linear and volume expansion for aluminum and gasoline are provided, and the volume expansion formulas are applied to determine the changes in volume. Initial calculations yielded an incorrect result, prompting a request for assistance. The correct answer is identified as 128 cm³, indicating a misunderstanding in the calculations. The discussion emphasizes the importance of correctly applying the volume expansion formulas for both substances.
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Homework Statement



A 3.00-liter aluminum cylinder at 5.00°C is filled to the brim with gasoline at the same temperature. If the aluminum and gasoline are warmed to 53.0°C, how much gasoline spills out? [Hint: Be sure to account for the expansion of the container. Also, ignore the possibility of evaporation, and assume the volume coefficients are good to three digits.

Homework Equations



Coeff of Linear Expansion for Al : 24 X 10^-6
Coeff of Volume Expansion for gasoline: 9.6 X 10 ^-4
Volume Expansion Formula: ΔV = βVoΔT

The Attempt at a Solution



I calculated the volume expansion formula for each variable and came up this:
aluminum = (24 X 10^-6)(3.00L)(53.0 - 5.00)°C = .003456
gasoline = (9.6 X 10^-4)(3.00L)(53.0 - 5.00)°C = .13824

I then subtracted (.13824) - (.003456) = .134784 = .135
And this is the incorrect answer... The correct answer is 128 cm^3 so I don't know what I am doing incorrectly...
 
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I figured it out - NM
 
how did you solve this problem?
 
jk27, please stand by, I or somebody will post some help in your thread.

p.s. Welcome to PF to both of you.
 
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