Step by Step Method of Solving Related Rates Problems - Conical Example

In this video we walk through step by step the method in which you should solve and approach related rates problems, and we do so with a conical example.
Before you start solving you should:
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1) READ the questions once, even twice.
2) UNDERSTAND what you need to find
3) WRITE what you are given + the equations for simple shapes
* Now you can start using the first step in the time stamp to jump ahead and see if you got the same answer as we did. If not you should watch the video from the beginning and NOT jump ahead*
TimeStamp !
1:34 - Solution begins. Press here only after you did the first 3 steps
3:37 - Second step. Find the "Volume of a Cone" - (Solution 5:13)
5:40 - Third step - Take the derivative of the volume with respect to time - (Solution 7:22)
7:35 - Fourth step - Find the rate at which the water level is rising by plugging "h" - (Solution 8:20)
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Now try to solve it on your OWN! Don't just "understand"... PRACTICE!!
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[@EthanVolochkov]

The "non-intuitive" step is what I was missing in an hours worth of going over this problem trying to relate height to radius... can't wait for the exam

[@Farah-ij2pw]

Not ganna lie, i was in tears before this video bc what the hell. BUT NOW I UNDERSTAND WHATS GOING ON, THANK YOU FOR NOT MAKING MY EYES TURN INTO WATER FALLS.

[@AFMathandEngineering]

We're glad we didn't make your eyes turn into waterfalls! Glad we could help!

[@jasminekoala4826]

I have a final for calculus in 2 days and you just saved me, my teacher made this seem much more complicated than it actually is. Great video!

[@afifakhan7288]

THANK UUUU I've been looking everywhere for someone to break down the steps

[@yasminhaq7958]

Thanks so much! I've been struggling with my homework and this is the first video that explained everything step by step.

[@sab9351]

POV: you’re watching this 2 hours before your AP test 👁👄👁

[@jonathanandy05]

I don't need the POV. I'm here with you, friend.

[@alaidbzqjsuegan6947]

sab were all here lmao

[@AFMathandEngineering]

Hope it went well...

[@jonathanandy05]

@@AFMathandEngineering Don't know about the other two, but it went great for me! No related rates though. Still a really helpful video!

[@emmageorge5246]

Tbf give me credit, ive got three hours.....

[@yeaboi7160]

this dude sound like tyler the creator with all these okay’s

[@blurscanner8078]

Thank you so much for explaining the steps and procedures (what are we looking for etc). Before this, I was stuck at a similar question and nearly gave up because I did'nt notice the similar triangle or implicit diff part...

[@meghancavanagh2376]

Very clear explanation and easy to comprehend. Thank you!

[@hel4259]

I would never have spotted the similar triangles! Thanks so much!

[@MrEric-rs2wg]

Thank's a Ton, You helped me remember something I totally forgot

[@joshlet]

Bigups to the AF MATH AND ENGINEERING TEAM. Thanks to your videos, I was able to smash my Canadian engineering equivalency test stemming from the degree I got in Pakistan. Look forward to more educational videos!

[@KishUnleahsed]

thisreally helped me more than the textbooks and my professor thank you

[@kennethumlas4737]

Thankyou for a Very Clear Discussion!!!

[@nihalbondugula3895]

Very helpful. Thank you so much!

[@swaggyskye]

Thank you!!!! this is the only video that does not confuse me and has a very decent pace lol

[@AFMathandEngineering]

Glad you enjoyed it!

[@lindseydouglas1913]

fam you just saved my life. bc we're out of school rn, my teacher decided to assign work that we were never taught ://///

[@AFMathandEngineering]

Classic

[@reyarjune7758]

Oh wow, really helped me out.Thank you for this video

[@nikitaartt8316]

Thank you so much, this really helped me I was on the verge of throwing my homework across the room because of this problem

[@atharvashah1129]

Great video, very clear!

[@jimcar53]

Thanks very much - perfectly explained

[@donmarz7030]

Thank you very much for posting this.🥰

[@ytp1210]

Best video that snapped me into my senses

[@AFMathandEngineering]

Excellent, glad to gear it! Thanks!

[@baitolesova24]

Thank you for simple explanation 😍👍👍👍👍

[@fzrynsha]

thankyou for making things clear 🤗

[@axemurderer27]

This was great. Really helped on my Calc assignments

[@AFMathandEngineering]

Glad it helped!

[@1light4love]

8:24 [YOU MEAN ITS NOT JUST MY CLASS?!??! ] (🙄all this time.... I just assumed my professor had past calculator trauma) WOW

[@AFMathandEngineering]

Yup I think for all Canadian universities calc type courses are no calculator

[@michaelazar8015]

Man is a real legend

[@EARLy0]

Well explained sir ❤️ thank you so much

[@LJTUBE06]

tnx for a clear explanation ❤

[@amaanahmed7376]

this was amazing thanks man

[@helseriddle2227]

Thank you sooo muchhhh

[@elisabethtausig7293]

THANK YOU!

[@akhilpaul7540]

It was helpfull..thank you

[@blessingshenjere484]

thank you

[@sanidugunathilake4183]

Thanks bro..

[@corntortillas673]

i have a project on related rates due in 3 days, thank u

[@cardtraderjay]

How do you decide what to put in the front of the equation, is it dV/dt all the time?

[@miriamminnesota1294]

You honestly helped me solve a problem i was struggling with so THANK YOU SO MUCH

[@thez5997]

One up watching this half an hour before mid term

[@AFMathandEngineering]

Hope it went well!

[@thez5997]

@@AFMathandEngineering well is a strong word 😂, let's just say better than it would have if I hadn't watched the video

[@AFMathandEngineering]

@@thez5997 Haha, glad we could help, if only a bit! I'm sure you did fine :)

[@ferdsmand_]

I didn't know this exact same question was written in our mastery test :o

[@AFMathandEngineering]

Hopefully you found this video before you wrote?

[@kitiaraiadelacruz5984]

hi very helpful video, i have a question, why is the final answer m/min when the given is m^3/min? thank you so much and God bless

[@shebbepss1282]

How it come up with pie over 12??

[@nhoxkid3863]

hi, can i asked you something? why does the rate of the water it's r/h not h/r why do we came with that formula ?

[@stephanplough]

If this tank were to be empty, how long would it take to fill up?

[@ai_a33_s]

This explanation for what stage?

[@mahoutsukai8956]

I don't know if you can help me out, but how would i solve a related rates problem, where the shape given is a right triangle, solving for the rate of change of an acute angle?

[@AFMathandEngineering]

Honestly, the best way to study for these types of problems is solve all of the different types from the textbook with the solution manual to help you if you get stuck. Most of them follow a very similar strategy with different relationships. That way whatever comes on the exam you'll be ready for.

[@juandissimomagnifico7819]

when you simplify the equation for volume after replacing the r with h/2, why does the 3 in the denominator turn to a 12 and not a 6?

[@juandissimomagnifico7819]

6:40

[@AFMathandEngineering]

The squared term applies to both the numerator and denominator in h/2, thus h^2/4, 4*3 = 12

[@chloeb4614]

Can I pay you to do my delta math hw? pls it's only 5 problems

[@derekwestbrook9383]

"they arent going to give this to you" tell that to my ap calc teach

[@niki-mendozacatalan5903]

When you are doing your ratio thing of the 2 triangles, why are you ignoring the 3m?

[@AFMathandEngineering]

We don't know what the radius of the cone is at 3m, we are given height and radius of the entire cone which serves the purpose of what we're trying to do: create a ratio of radius to height solve for r and plug in eliminating r. 3m is used at the end of the video to solve for the rate.

[@karanjot0009]

❤❤

[@karlodominicmanangan7579]

Thank you so much bro😭😭 (tears of joy)

[@AFMathandEngineering]

Glad theyre joyful tears haha! Thanks for the comment!

[@bellissmith9379]

i wish i could say i understood, i do understand the steps but not the math and how you were getting the derivatives

[@meaningful2366]

Well, you'd need to understand how to take derivatives to be able to understand it. Once you understood how to do the derivatives, then it'll make sense a lot. I suggest watching youtube videos on how to take a derivative because they're pretty basic if you just remember the rules.

[@phucdang1095]

how is r/h=2/4? i understand where you got the two but what about the four?

[@AFMathandEngineering]

4m is the full height of the cone

[@phucdang1095]

How did you get 4?it doesnt say that in the problem.

[@AFMathandEngineering]

Theres a dimension line that shows 4m directly on the drawing

[@phucdangchannel]

@@AFMathandEngineering how is it pi/12?

[@AFMathandEngineering]

@@phucdangchannel h*pi*(1/3)*(h/2)^2 = h*pi(1/3)*(h^2/4) = pi/12 * h^3

[@jetleeyonque1636]

how did r become h/2? when solving r/h = 2/4?

[@jetleeyonque1636]

nvm found out. if anyone's wondering he did fraction and solved for r.

[@xinloongfoo2951]

'WHEN THE WATER IS 3 METER DEEP' where is it?

[@AFMathandEngineering]

X Gamers when we solve for the derivative of the volume as a function time, we plug in 3 meters for h. This gives us the rate at which the water is rising per minute. This step is near the end of this video. Hope that helps!

[@clarizaatillo1839]

How to simplify the v formula? You said step by step?

[@AFMathandEngineering]

If you can't simplify algebraic formulas you're in trouble LOL

[@wanderleyapparecidovieira2282]

OK,but find a way out to put your hands not in front when writing ! ( kudos and corrections )

[@Waxahachie666]

I'm from 5th grade and I understand this

[@junaidiqbal3999]

Given Height Is 4 but you put 3 in h how ?

[@AFMathandEngineering]

Problem wants us to solve for rate when water is 3 meters deep, hence 3m.

[@chidivids2005]

I always forget that goddamn first thing😤

[@dcracecar3024]

saved my ass

[@Waxahachie666]

I will surprise my fake friends ty

[@psylachelseyalvarez5512]

That was not step by step

[@phucdang1095]

it was step by step.You are mexican and too stupid to understand.That's how you show your work.

[@talh1099]

Phuc you

[@DrewEricNoftle]

1:43 in and all he has done is read the question...

[@romtuico]

thank you

[@AFMathandEngineering]

No problem!