Related Rates Cone Example (Calculus)

This video is about Calculus Related Rates. We discuss some practical steps for approaching related problems such as: Drawing a diagram, write down what you know and what you want to find, writing an equation relating the variables, implicit differentiation, solving for the unknown quantity. We look at a related rate problem involving a cone in this math video tutorial by Mario's Math Tutoring.
0:12 Example 1 Related Rate Calculus Cone Problem
0:42 First Step is to Draw a Diagram
1:02 Second Step Write Down What We Know and What We Want to Find
1:42 Third Step Write an Equation that Relates the Knowns with Unknowns
1:55 Using Similar Triangles to Write a Proportion
3:23 Substitute to Get Everything In Terms of h
4:01 Do Implicit Differentiation With Respect to Time t
4:47 Substitute Known Values and Solve For Unknown
Related Videos:
Calculus Related Rate Ladder Problem
• Related Rates Ladder P...
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[@mekam3963]

Gosh darn it that triangle trick helped a BUNCHHH!!! Thanks!!!

[@MariosMathTutoring]

You’re welcome Sher! Glad my video helped you!

[@RinaNewhouse]

Clear as day explanation. Thank you so much.

[@stjarna5072]

This is what I've been looking for 🥰🥰 Thank you so much sir!!

[@thirdly5509]

Since you know that r=3h/4, why didn't you substitute the given h=3? That will make r=9/4 right? Is there a reason behind why you haven't made this method? I am confused. I hope you see this. Thanks!

[@abcggg12345678]

Generally, you don't plug in the specific information of h = 3 until after you have the relationship established. If you substitute h = 3 in right away before you compute the RATES, then you are saying that the depth of the water is always 3 for the entire problem. But it is not. As you continue to add water into the tank, the depth continues to change as does the RATE at which the depth is changing. Think about it this way: When the tank is almost empty, and you pour water in, the depth will be increasing very quickly. But when the tank is nearly full, it's a lot wider near the top, and you keep pouring water in at the same rate, the depth is barely changing at that point and seems like it is rising very slowly. Anyways, the first step is to find a relationship between the RATES for the Volume and the Height. After you take a derivative and then have that relationship, finally you can substitute in for the specific depth.

[@SizzleStreams]

I was wondering the same thing lol

[@johnsteel8421]

Thanks sir 🙏 I really wanna to appreciate you

[@MariosMathTutoring]

So nice of you

[@chaenglaurent11]

Hi sir mario. Big fan of your videos. Much love here from philippines. Filipinos are the best

[@MariosMathTutoring]

Glad you like my videos and channel! Thanks for being part of the channel!

[@minato4294]

Here I am studying for my calc final and I see this and can’t stop laughing. That’s awesome

[@praneshbalasubramaniam8749]

thank you ser

[@MariosMathTutoring]

You’re welcome Pranesh!

[@allaindeleon4452]

so the answer is 6.21 rounded to the nearest hundreds

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