Related Rates Problem

  • Thread starter tangents
  • Start date
  • #1
tangents
21
0
Hey guys, I'm having some trouble figuring out this problem and was wondering if someone would be kind enough to look over my work so I know that I am doing it correctly =).
-------------------------------------------------------------------------

There is an open right cylinder cone that has a heigh of 10cm and diameter of 10cm. the depth h is changing at -3/10cm/hr. V=1/3(pi)r^2(h).

a) find volume of water at h=5

V= 1/3(pi)(5^2)(5)= 125/3(pi)cm^3

b) find dv/dt when h=5cm

dv/dt= 1/3(pi)(5^2)(-3/10)=-5/2cm^3/hr

c) show that rate of change of volume of water is directly proportional to the surface area of water. what is the constant of proportionality

dv/dt=1/3(pi)r^2(dh/dt)
surface area=(pi)r^2
1/3(pi)r^2(dh/dt)=(pi)r^2
constant is (pi)r^2
---------------------------------------------------------------------

My main problem is with parts b and c as I'm not sure if I am getting the concept of related rates correctly =/
 

Answers and Replies

  • #2
mathmike
208
0
for one you must understand that diamater of the cone is changing with the height.
 
  • #3
tangents
21
0
yes I figured that since the height decreases, so does the radius except the problem didn't give me dr/dt or any real mention so I'm not sure how to apply it to the problem if I need to.
 
  • #4
mathmike
208
0
well since the diameter is 10 when the height is 10 you can define one of them in terms of the other one, then you can take the derivitave wrt that variable. do you know how to do this?
 
  • #5
HallsofIvy
Science Advisor
Homework Helper
43,021
970
Draw a picture. The side of a cone is a straight line so you can use "similar triangles" to find the function relating r to h (or just find the equation of the line through (0,0) and (10, 5)).
 

Suggested for: Related Rates Problem

Replies
1
Views
593
  • Last Post
Replies
19
Views
923
Replies
2
Views
147
Replies
30
Views
2K
  • Last Post
Replies
11
Views
907
Replies
13
Views
628
  • Last Post
Replies
3
Views
892
Replies
22
Views
2K
Replies
2
Views
289
Top