Solving for the Length of a Cubical Tank using Related Rates

[shortman12012]

Homework Statement

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?

Homework Equations

v=L^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

 

[Syrus]

1 Liter is a cubic decimeter

 

[shortman12012]

1 liter is also 1000 centimeters^3

 

[Ray Vickson]

Homework Statement

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?

Homework Equations

v=L^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

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

 

[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?