Math Help - Volumetric expansion problem

1. Volumetric expansion problem

Hello, i understand this isnt a calculus question but there seems to be the most people on this forum. Im studying for my Power Engineer 3rd class and have a question. At 5 degrees celcius a steel tank with a diameter of 9m and 6m height, is filled with oil at the 5.9m level. at what temperature will the oil overflow by 3.4m cubed? Do not forget steel expands as well. Coefficient of linear expansion Steel- 12x10-6 (to the power)
'' '' Volumetric expansion oil - 4.1x10-4

change in volume= original volume x coefficient of expansion x change in temp.

answer given in back of book 71.7 degree C

If anyone can show me how to figure this one out, that would be great

Cheers

2. Re: Volumetric expansion problem

If we have

$l=l_0(1+{\alpha} \;{\Delta} t)$.

The volume is

$V=V_0(1+{\alpha} \;{\Delta} t)^3$.

Or with some approximation

$V=V_0(1+3{\alpha} \;{\Delta} t)$.

3. Re: Volumetric expansion problem

The volume of the oil Vo as it expands, is given by the first equation, t is the temperature increase.
The second equation is the volume of the tank as it expands plus the extra 3.4 cubic meters.

The temperature t at which Vo = Vt can be found by graphing the two equations and finding the intersection.

I found the intersection at 68 deg. Plus 5 deg is 73 deg. 2 deg off from your answer.