# 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

## Answers and Replies

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

HallsofIvy
Science Advisor
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
Science Advisor
Homework Helper
Why do you think the answer is wrong?

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

Dick
Science Advisor
Homework Helper
I can't see where it's incorrect. Except for technicalities. They ask for the rate at which it is decreasing. So you would be technically correct to put in a positive number. This 'online' things can be complete idiots.

cristo
Staff Emeritus
Science Advisor
Have you checked the units the online thing wants the answer in?