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Related Rates problem

  1. Aug 23, 2011 #1
    1. The problem statement, all variables and given/known data
    Water flows into a cubical tank at a rate of 19 L/s. If the top surface of the water in the tank is rising by 3.7 cm every second, what is the length of each side of the tank?


    2. Relevant equations
    v=L^3


    3. The attempt at a solution
    so what I started doing was

    dV/ds = 3l^2 dl/ds
    changed 19 L/sec into cm^3 which is 19000
    19000 = 3l^2(3.7)
    19000 = 11.1l^2
    divided both sides by 11.1
    1711.71 = l^2
    then took the square root of both sides to get
    41.37 cm
    however when i put in the answer for my homework, it says the answer is wrong, i have 10 tries, so i was wondering what am i doing wrong or what is the right way to do this problem
     
  2. jcsd
  3. Aug 23, 2011 #2
    1 Liter is a cubic decimeter
     
  4. Aug 23, 2011 #3
    1 liter is also 1000 centimeters^3
     
  5. Aug 23, 2011 #4

    Ray Vickson

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    Science Advisor
    Homework Helper

    Sometimes, in problems like this one, you get nothing but trouble if you use units within your equations. It is better to express things like this: the inflow rate is V liter/sec, where V = 19. (Here, V is dimensionless.) If the sides of the tank have length x cm, the flow rate in cm^3 per sec is 3.7*x^2. (Note: here, x is dimensionless, as is the 3.7, because I said the width was x cm and 3.7 is the number of cm per second.) Now just clear up liters vs cm^3 and you are done.

    RGV
     
  6. Aug 23, 2011 #5
    sorry but i'm not following you on your explanation. I understand about taking out all the units, but then where did you get 3.7*x^2 from and what is the final equation you are using?
     
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