# Chain rule

A cubical block of ice is melting in such a way that each edge decreses steadily by 8.8 cm every hour. At what rate is its volume decreasing when each edge is 5 meters long?

this is my work

Let l=l(t) be the length of each edge at time t

then volume = l^3
dl/dt = 8.8cm/h = .088m/h

dV/dt = dV/dl * dl/dt
= 3l^2 * .088 m/h

at l = 5
dV/dt = -6.6m/h

where have I made an error?

thanks

Dick
Homework Helper
I don't see any problem except the units. volume/time isn't m/h.

HallsofIvy
Homework Helper
Early on you should have dl/dt= -0.088 m/h but you appear to have put the negative in the final answer. Dick is correct: You need to keep better track of your units. 3 (5 m)2= 75 m2. Multiplying that by -0.088 m/h gives -6.6 m3/h which is correct, of course for rate of change of volume since volume is measured in m3 so the rate of change of volume per hour is m3/h.

sorry i put in -6.6m^3/h
thats just a typo

i'm still getting the wrong answer?

Dick
Homework Helper
Why do you think the answer is wrong?

inputting it for an assignment online and getting an "incorrect" response

Dick