Calculus applications of derivatives problem: Draining Conical Reservoir

[orne0726]

Hi can someone please help me with part a, i have the volume equation but i can’t figure out where i am supposed to go from there.

17. Draining Conical Reservoir Water is flowing at the rate of 50m^3/min from a concrete conical reservoir (vertex down) of base radius 45m and height 6m. (a) How fast is the water level falling when the water is 5 meters deep? (b) How fast is the radius of the water's surface changing at that moment? Give your answer in cm/min.

 

[Harry_the_cat]

First of all, check your formula for volume!

 

[Steven G]

You need to use similar triangles to get a relationship between r and h so you can write the volume (correctly!) just in terms of h--h because they give you dh/dt.

 

[Steven G]

Part a and b looks fine.

I think that before multiply you should try to reduce first. I suspect that in your case, this means to stop using your calculator. It basically just take more time most of the time.

 

[Harry_the_cat]

I've attached a scan with the work that i wrote out for this problem. I'm happy to message more if you'd like me to explain in greater detail.

For answers, i got the following:

a) dh/dt = 0.045 cm/min when h = 5 m
b) dr/dt = 8.5 cm/min when h = 5 m

@MathTutorPro

Most of us who help on this site are more than capable of providing a complete solution to problems such as this one. However we choose not to. Providing a fully worked solution is not the policy on this site and does not really help the student in the long run. A professional maths tutor would understand that.

We try to guide the student by asking what they have done, where they are stuck and giving them hints along the way.

Notice that the original poster asked for help, not a complete solution.

When a poster asks upfront for a complete worked solution, it is most often because they are going to submit it for credit - that's cheating. We certainly don't condone that.

I see you have just joined this site and probably mean well, but you are likely to get banned if you continue to provide complete solutions.

 

[Harry_the_cat]

Part a and b looks fine.

I think that before multiply you should try to reduce first. I suspect that in your case, this means to stop using your calculator. It basically just take more time most of the time.

Just bringing to your attention Steven G that Post #3 was not posted by the OP.

 

[Steven G]

I've attached a scan with the work that i wrote out for this problem. I'm happy to message more if you'd like me to explain in greater detail.

For answers, i got the following:

a) dh/dt = 0.045 cm/min when h = 5 m
b) dr/dt = 8.5 cm/min when h = 5 m

MathTutorPro,
Welcome to the forum. Please read the posting guidelines. It clearly says that since this is a math help forum we don't just give out answers, especially to someone who showed no work at all. This is not my rule nor do I necessarily agree with it, but if you continue to violate the posting rules you will be banned from the site. In the future just give helpful hints so that the student can learn from this forum.