For every $3^\circ$ rise in temperature, the volume of a certain gas expands by $4$ cubic centimeters.  If the volume of the gas is $24$ cubic centimeters when the temperature is $32^\circ$, what was the volume of the gas in cubic centimeters when the temperature was $20^\circ$?
$\text{(A)}\ 8 \qquad \text{(B)}\ 12 \qquad \text{(C)}\ 15 \qquad \text{(D)}\ 16 \qquad \text{(E)}\ 40$
We know that 
\[T=32-3k\Rightarrow V=24-4k.\]
Setting $k=4$, we get the volume when the temperature is $20^\circ$, which is $24-4(4)=8\rightarrow \boxed{\text{A}}$.