So here is the question I'm having a bit of trouble with!

"The Coast Guard is monitoring a giant iceberg in the approximate shape of a rectangular solid that is five times as long as the width across the front face. As the iceberg drifts south, the height above water is observed to decrease at the rate of two metres per week, and the width across the front is shrinking at three metres per week. Find the rate of loss of volume above the water when the height is 60m and the width of the face is 300m."

So here has been my approach towards this question, I end up getting an answer, but it's not correct :(

My approach:

I know that $l$=$5w$ and $\frac{dw}{dt} = \frac{-3m}{week}$ and $\frac{dh}{dt} = \frac{-2m}{week}$

So now I rearrange the volume formula for a rectangular prism, using $l=5w$ to $V=5w^2h$.

Now I take the new formula for the volume of a rectangular prism and differentiate it to get: $\frac{dV}{dt} = 10w\frac{dw}{dt}h + 5w^2\frac{dh}{dt}$, then subbing in all the terms, $w=300m$ and $h=60m$ along with the other rates listed above, I get $\frac{dV}{dt} = 10(300)(-3)(60) + 5(300)^2(-2) = -1440000$.

But at the back of the book, it says its $-901800m^3/week$...so what am I doing wrong?

Please and thank you everyone!


1 Answer 1


I see two typos: the first parenthesis should be $300,$ not $600,$ and your result comes out (with that correction) to $-1,440,000.$ I agree with your answer. As a check, $300 \cdot 1500 \cdot 60-297 \cdot 1485 \cdot 58=1,413,000$ where I just applied the reductions.

  • $\begingroup$ I was just wondering, where you did you get 297⋅1485⋅58 from? So I'm doing what I should be, so there is potential that the textbook is wrong? $\endgroup$
    – user70871
    Jun 17, 2013 at 1:26
  • $\begingroup$ @user70871: I think you have the right approach and the text is wrong. My check was just to take 2 off 60 to get 58, 3 off 300 to get 297, and make the length 5*297. This is not the instantaneous rate, which is what you have. But it is the change in volume in one week, which should be close, and is. $\endgroup$ Jun 17, 2013 at 1:32

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