Related Rates problem

  • #1
shortman12012
13
0

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
 

Answers and Replies

  • #2
Syrus
214
0
1 Liter is a cubic decimeter
 
  • #3
shortman12012
13
0
1 liter is also 1000 centimeters^3
 
  • #4
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
10,706
1,722

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
 
  • #5
shortman12012
13
0
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?
 

Suggested for: Related Rates problem

Replies
1
Views
595
  • Last Post
Replies
19
Views
926
Replies
2
Views
156
Replies
30
Views
2K
  • Last Post
Replies
11
Views
910
Replies
13
Views
630
  • Last Post
Replies
3
Views
894
Replies
22
Views
2K
Replies
2
Views
291
Top