Related Rates - Gravel Dumped Into Conical Tank Problem

This calculus video tutorial explains how to solve problems on related rates such as the gravel being dumped onto a conical pile or water flowing into a conical tank.
Introduction to Limits: • Calculus 1 - Introduct...
Derivatives - Fast Review:
• Calculus 1 - Derivatives
Introduction to Related Rates:
• Introduction to Relate...
Derivative Notations:
• dy/dx, d/dx, and dy/dt...
Related Rates - The Cube:
• Related Rate Problems ...
__________________________________
Inflated Balloon & Melting Snowball:
• Related Rates - Inflat...
Gravel Dumped Into Conical Tank:
• Related Rates - Gravel...
Related Rates - Area of a Triangle:
• Related Rates - Area o...
Related Rates - The Ladder Problem:
• Related Rates - The La...
Related Rates - The Distance Problem:
• Related Rates - Distan...
____________________________________
Related Rates - Airplane Problems:
• Related Rates - Airpla...
Related Rates - The Shadow Problem:
• Related Rates - The Sh...
Related Rates - The Baseball Diamond Problem:
• Related Rates - The Ba...
Related Rates - The Angle of Elevation Problem:
• Related Rates - Angle ...
Related Rates - More Practice Problems:
• Related Rates - Conica...
_________________________________
Final Exams and Video Playlists:
www.video-tutor.net/
Full-Length Videos and Worksheets:
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[@TheOrganicChemistryTutor]

Next Video: kzbin.info/www/bejne/iHi1mZykdpyMeqs Final Exams and Video Playlists: www.video-tutor.net/

[@user-qd6wm5cz1o]

#1 Most Soothing Voice

[@heathuschrist3108]

This video was super helpful. Thank you for helping myself and others to learn how to tackle these pesky word problems!!

[@apexdisease6030]

You explain this better than anyone else Iv'e watched, thank you

[@georgesadler7830]

MR. Organic Chemistry Tutor, thank you for a fantastic video/lecture on Related Rates in Calculus One. I always have some problems with Related Rates word problems; however, my overall understanding of this topic is improving. This is an error free video/lecture on KZbin TV with the Organic Chemistry Tutor.

[@nathanheide8937]

massively helpful explanation for a complex problem. thank you!

[@alexmoorehead8501]

I'm sure I'll understand how to do these myself eventually :(

[@allahkaboom1860]

Did you figure it out? 😂

[@IrvinMenezes]

You got this bro

[@finnmurphy2177]

we believe in you

[@hoshicakes3]

You can do it pal

[@jackcarraway4707]

Think of it this way: related rates is literally just geometric formulas (usually volume) with dx/dt and dy/dt thrown in. Note the shape in question, pull its volume equation and make your list.

[@souadelferjani]

Dude you saved my whole semester

[@blueastro4722]

Why do you always have a video of every problem I have? Thank you so much

[@jimcar53]

Thanks so very much - you are a fantastic teacher.

[@mathwithnour9780]

شكرا يارجل امثلتك رائعة وكثير استفاديت منها Thank you, man. You have been very helpful and your examples are wonderful

[@YRO.]

صحيح

[@dankplayz4243]

You work your ass off on youtube and i thank you for that since it helps me with my math needs i am looking forward to your next vid and i hope you do some gaming i think that would be preatty cool but if you want to stick with math i respect that i hope you get 1 mill one day so just keep doing what you are doing and youll get there!

[@andrewyoung4473]

2.1 million now, he did it! He deserves it, he is so helpful!

[@susa9786]

3.77 mill, my friends! He deserves more, I'm happy for him 😭👌🏼

[@firezahin1]

@@susa9786 3.83

[@nicholegordon9868]

@Montemi 4.64M :')

[@pahoellyyy]

5.33M now!

[@qifanyang404]

Super helpful!! Thank you so much!

[@sit772]

when i hear this man’s voice all my worries fade

[@jasminekoala4826]

Studying for my calculus final and this video has saved my life, my teacher isn't the best at explaining things lol

[@NeillMikha]

It is very clear thank you!

[@coremath.]

bro i love you so much how do you have a video FOR EVERYTHING thank you 🙏

[@---hf5kb]

In the area of triangle video, there are 2 different variables (b and h) in the rate equation. In this video, why do you have to convert radius in terms of height? Can't you solve the rate of 2 variables (radius and height) too in the equation?

[@daviddavid5143]

I think the water tank in the last problem will be empty soon but thank you very much for the efforts. Best tutor ever.

[@heranh9440]

Great job !

[@richardvillanueva1782]

Thank you so much !!

[@andrewgilbert7762]

When you created the ration of the height to the diameter you didn't use the cm values for the h and d, and you later plugged in cm values for h and dh/dt. Is that a mistake?

[@ibrahimalowonle9106]

Thank You So Much👍👍👍

[@bradreed2001]

Arigato math senpai!!!

[@Geert305]

This is so good

[@mrfatboy327]

I had completely forgotten that a ratio is a constant.

[@fulin_coban]

love u dude

[@mahoutsukai8956]

How would I solve for the rate of change in the radius of a cone when the radius is three times the height? (Values given: r=3h, dv/dt=20 ; solve for dr/dt when V=200)

[@samuellim2293]

Mario Valle sane thing but you would just substitute 3h for r in the formula for the volume of a cone

[@NOVAGRACEBENOJO]

question why do we need to calculate for the net

[@badz416]

in the 1st question, why would you multiply 3x12 if the 12 was cancelled ?

[@Jeremy_Fisher]

It's because it was squared. He likes to cross off the number when it cancels even if it's squared but I and many people find that confusing.

[@johnrperry5897]

Yeah that's super confusing. Glad you caught that. I thought I didn't understand basic math for a second.

[@BillyBob-tr5cv]

Holy crap. Your way is so much easier.

[@Nemoguzapomnit]

I can't get - why is the Net volume flow rate = the rate at which water is flowing into - the rate at which water is flowint out?

[@alexhachey1806]

Bro how?

[@rentothemaxx]

I don't understand why you do a ratio of h/d. why do you pick h/d and not d/h? how do you determine that?

[@semicloudy]

It doesn't matter whether you use h/d or d/h, but keep in mind if you decide to use d/h, you have to flip 8/6 to 6/8 so the proportion makes sense.

[@taotaofu9331]

So we don't need to use dh/dt in practice 2, it's useless?

[@khalidhassani6173]

Why not replacing R by 3 in 10:17 ?

[@sylargrey7034]

For the last question shouldn't the dv/dt [in] be greater than the dv/dt [out]? Since the dv/dt [out] is being leaked out it should be considered negative right? Therefore making the last equation to solve equal to dv/dt [net] = dv/dt [in] - (-)dv/dt [out]. Then solving for the dv/dt [in] you get -11642 cm^3/min. But you can just flip the signs. To make it -7500, and +11642.

[@peterhindes56]

The height is decreasing. Water is being lost.

[@tobyklauder2370]

honestly you own my GPA

[@jmgroup1434]

Hi, for the 2nd question, why didn't you convert the height and diameter to centimeters before finding the ratio?

[@Aerospace63]

Well, his explanation almost helped. If he can’t help no one can I’m screwed

[@Daksh-mx5ds]

In the first problem did you mean 1/18pi feet cubed per minute instead of feet per minute?

[@superduperdil]

the only thing worse than calculus is mike bloomberg ads.

[@yeezuschrist420]

Can’t argue with that lmao

[@jadabicensio3099]

Why did you multiply 3 by 12 after dividing it by the 12 below 25?

[@alexadamasceno9409]

jada bicensio bc the 12 was squared but there was a twelve in the denominator so he cancelled that out and was like left with just 12

[@holopleasures4011]

I am confused as to why he couldn't just use d=2r and put it in terms of r. so, r =D/2 then take the diameter (6) and divide it by two.

[@justinsantos5751]

You can't substitute r with diameter because when you take the derivative of the volume with d in it, you'll have d(d)/dt which is bot given. That is why it has to be in terms if h or height because the d(h)/dt is given.

[@justinsantos5751]

Not* given

[@alexts94]

I'm still not really understanding the units. Why is dh/dt not ft^3/min? At 5:53

[@aliissamthanoon1603]

height not volume

[@zack_120]

Why repeating "V =" while one of them is enough, with the subsequent Eqs. just led by a "=" WITHOUT THE "v"? In other words, only ONE V is needed at the beginning. That way, it clearly shows that it is the SAME "V=" in the entire series. If "V=" is repeated, it easily projects an confused impression that the term may have changed.

[@doronq1847]

Done

[@yamaldunar1574]

Are we supposed to convert the h= 8m and diameter= 6m to cm? Because in this video, it was shown unchanged and used as a deriviation of value.

[@prabakaransivakumar1297]

you don't have to convert most of the units of measurements in this unit.

[@GamerDemonz]

the ratio of the h and d stays constant between units, thats way these are called constants. for example 1 cm / 2 cm = 0.5 and .01 m /.02 m = 0.5, the overall ratio stays the same.

[@its_zaheer7244]

lol. midterm is tmro and i still cant intuituely complete these :/

[@mauricejones5286]

R = 3m, but you used 25cm for the height… im confused, did you not need to convert the 3 over to cm as well?

[@Max-cu6bw]

No, because he already converted radius to diameter and then got the diameter in terms of height. Once he had this, the only value he had to to convert was the height since it was the only variable he used.

[@Max-cu6bw]

If you see the conversion he made from diameter to radius and then radius in terms of height, if you convert the height and diameter to cm from meters you get 800cm and 600cm, and solve the equation, you will get the same result either way because you are just applying it to the 25cm that he got as h

[@alliepierce2471]

these are so hard bruh

[@tylerdickieson9361]

im always running outta space too man

[@Altair4611]

Breaking news: he ran out of space

[@beatsforeveryday5314]

Calc exam in 3 hours 🙃

[@thesamuelrios2181]

i dont understand any of this.

[@omaralmadani4580]

Its so easy. Watch his other related rates in order to understand this one more

[@yanimiller5856]

What is dv and dt ?? This is so confusing there has to another way then this...

[@a7medabdelsalam775]

dv is the derivative of volume and dt is the derivative of time

[@joshuasanders644]

watch his video called introduction to related rates

[@justinsantos5751]

It is just a notation for the rate at which the v or volume changes with respect to t which represents time

[@imperialrecker7111]

there is another way. Try making the experiment. 😂

[@yanimiller5856]

Imperial Recker 🤣 this is a year ago thanks I got it

[@theobserver314]

I am not sure why I read "Gravel Falls" as "Gravity Falls."

[@dolagygad8763]

please find a way to raise your voice in the videos!!

[@FrankFurther]

As much as I appreciate these videos, please stop using feet and use SI units.

[@jacoblee9765]

Ben Tate The unit used in calculus is feet, because, unlike physics and other sciences, it was not invented in Britain, the UK, or one of the other countries over there.

[@leobesa2887]

Yep i would agree, BUT professors will almost always use English units to make the problems more difficult for the students. Smh.

[@Zightz]

@@jacoblee9765 Um, where do you think you got your imperial units from? The UK is the only place in europe still not using metric.

[@jacoblee9765]

Zightz Calculus was invented in the United States, where the unit used is feet.

[@Zightz]

@@jacoblee9765 Oh, really? Thanks for clearing that up

[@MRKITTY-yi5iw]

this makes no sense thanks tho

[@OFNBW]

Your accent is weird

[@coldestsun2095]

Your username is weird

[@OFNBW]

@@coldestsun2095 Touche