Thermal expansion, cup overflowing?

[azurken]

Homework Statement

Coefficient for thermal expansion for glass is β1 = 25x10^-6 K^-1
Coefficient for thermal expansion for this particular liquid is β2 = 300x10^-6 K^-1

The glass cup is completely filled with the liquid at 4.0 L. The temperature of the glass and liquid both increased by 10C^o

Homework Equations

ΔV=(V)(β)(ΔT)

The Attempt at a Solution

Alright. I know there's a difference between 10 C^o and 10^o C. Because how can (for example) 58^o C - 57^o C ≠ 274k. So I counted the K as exactly C one for one.

(4L)(25x10^-6 )(10) = 0.001L (I cancel out the temperature units here)
(4L)(300x10^-6)(10) = 0.012L (cancel out temperature units)

So the liquid will spill 0.011L over the cup.

I'm just not sure how I should I convert the coefficients to the celsius numbers (unless I did it right)

 

[Asim Riaz]

and if I'm right, I'm not sure how to get the difference in volume between the two with the numbers I found.