Chain rule

  • Thread starter Destrio
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  • #1
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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

  • #2
Dick
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I don't see any problem except the units. volume/time isn't m/h.
 
  • #3
HallsofIvy
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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.
 
  • #4
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sorry i put in -6.6m^3/h
thats just a typo

i'm still getting the wrong answer?
 
  • #5
Dick
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Why do you think the answer is wrong?
 
  • #6
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inputting it for an assignment online and getting an "incorrect" response
 
  • #7
Dick
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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.
 
  • #8
cristo
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Have you checked the units the online thing wants the answer in?
 

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