Rate of change - cones

by jsmith613
Tags: cones, rate
 P: 614 1. The problem statement, all variables and given/known data I have attached a link along with my working please can someone help me http://s359.photobucket.com/albums/o...rrent=Math.png 2. Relevant equations 3. The attempt at a solution
Mentor
P: 19,694
 Quote by jsmith613 1. The problem statement, all variables and given/known data I have attached a link along with my working please can someone help me http://s359.photobucket.com/albums/o...rrent=Math.png 2. Relevant equations 3. The attempt at a solution
Please post the problem and your work here. IMO, it's a pain in the butt to have to open a web page to see the problem and the work, plus I can't insert a comment at the appropriate place where there's an error.
P: 614
 Quote by Mark44 Please post the problem and your work here. IMO, it's a pain in the butt to have to open a web page to see the problem and the work, plus I can't insert a comment at the appropriate place where there's an error.

dv/dt = 4 cm3 min-1

tan(60) = r/h

r = √3* h

V = (1/3) π r2h

dv/dh = (1/3) π r2

dh/dt = (dh/dv) * (dv/dt)

= 1/(1/3) π r2 * 4

= 12/(pi r2)

for h = 4

dh/dt = 0.079577

The answer given is 0.0265 cm/min. why?

I don't know how do use latex - see post for a clearer solution if you get lost!

P: 614

Rate of change - cones

question was:

A hollow cone with a semi-vertical angle of 60 degrees is held vertex down with its axis vertical.
Water drips into the cone at 4 cm3/min
Find the rate at which the depth of water is increasing when the water is 4 cm deep
Mentor
P: 19,694
 Quote by jsmith613 dv/dt = 4 cm3 min-1 tan(60) = r/h r = √3* h V = (1/3) π r2h dv/dh = (1/3) π r2
You're ignoring the relationship between r and h.

Substitute for r in your volume equation. Then you'll have V purely as a function of h.
What you have is not correct, because V is a function of r and h.
 Quote by jsmith613 dh/dt = (dh/dv) * (dv/dt) = 1/(1/3) π r2 * 4 = 12/(pi r2) for h = 4 dh/dt = 0.079577 The answer given is 0.0265 cm/min. why? I don't know how do use latex - see post for a clearer solution if you get lost!

 Related Discussions Electrical Engineering 1 Calculus & Beyond Homework 1 Precalculus Mathematics Homework 8 Calculus & Beyond Homework 5 Chemistry 3