# Related Rates problem

1. Aug 23, 2011

### shortman12012

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. Aug 23, 2011

### Syrus

1 Liter is a cubic decimeter

3. Aug 23, 2011

### shortman12012

1 liter is also 1000 centimeters^3

4. Aug 23, 2011

### Ray Vickson

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

5. Aug 23, 2011

### shortman12012

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?