Rate of Volume Decrease of a Cubical Block of Ice

[Destrio]

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]

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

 

[HallsofIvy]

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.

 

[Destrio]

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

i'm still getting the wrong answer?

 

[Dick]

Why do you think the answer is wrong?

 

[Destrio]

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

 

[Dick]

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]

Have you checked the units the online thing wants the answer in?