I am having problems correctly solving the given question, in which I must solve for $V$, $\frac{dl}{dt}$ for cm/h and m/h, $l$ and the rate of change:
A cubical block of ice is melting in such a way that each edge decreases steadily by 5.5 cm every hour. At what rate is its volume decreasing when each edge is 10 meters long?
My solution is:
$V = l^3\\ \frac{dl}{dt} = 5.5_{cm/h} = 0.055_{m/h} \\ \frac{dV}{dt} = 16.50_{m^3/h}$
where $\frac{dV}{dt} = 3(l)^2 \frac{dr}{dt} \\ = 3(l)^2 (0.055) \\ = 16.50$
Please notify me on any missteps I have made as this is the incorrect solution to the given problem.
The answer (and $\frac{dl}{dt}$) should be negative. Remember, the sides and volume are decreasing, so the derivatives should be negative.