Calculus 1: Max-Min Problems (10 of 30) Largest Cylinder that Fits in a Circular Cone
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- Опубликовано: 30 сен 2024
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In this video I will find the largest volume=?, cylinder that fits into a right circular cone where h=20cm and r=12cm.
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• Calculus 1: Max-Min Pr...
Hello Michel, thanks for all your lectures, very interesting.
For this one, I tried use Thales theorem to express R with respect to H, so I get H=5/3R. When I use this value of H in the cylinder volume's equation, after derivative, I obtain V' = 0 only for R=0.
I understand I found a min instead of a max, but it's quite disturbing to me.
When there is several constraints possible, is there a tip to know which one we have to choose ? Or you just have to try one constraint in order to discover it wasn't the one who works until you find the right one ?
Regards,
why do we need to use slope instead of hypotenuse?
i think Vcone = 1/3(pi)(12)^2(20)=3015.93 and Vcylinder=(pi)(8)^2(6.67)=1341.08 is the answer sir
This is also what I got,,, small mistake by Michel,,, I enjoy his very well explained approach to maths.
Vcylinder = 1340.41
@@cookieboi4449 i think we do not use the volume of cone to solve this problem
why m = -20/12 and not just 20/12
m represents the slope and in this example the slope is negative
AoA ........sir ur online lectures are very beneficient for me ......... and also i feel improve ur self......i request to u sir please upload in electrical engineering chapter 9 to chapter 16 lectures these chapters are missing please upload them......thank u sir.
It is on the stack of videos to complete.
Thank you. I got some very important directions on how to think when I face these kinda problems.
Glad you found it helpful.
why do we need to use slope instead of hypotenuse?
Thank you so much! You are my lifesaver
Happy to help!
prf thanks alot ı want to ask one questıon y=mx+c where -12 from thanks?
The slope of the side of the cone = rise / run = (-20 cm) / (12 cm)
Saved my mid-term ! Thank you
Glad you found the videos helpful. 🙂
why do we need to use slope instead of hypotenuse?
if u don't like this method u can use similiar triangle
12-R/12 = = 20-H/20 or
20/12 = 20-H/12-R
slove for H or R and the remaining is same
sir , how can we do it for a cylinder inscribed in a sphere
It would work the same way except that the equation of a circle is: x^2 + y^2 = R^2
Thank you.
You're a good teacher
We appreciate the comment. Glad you like our videos. 🙂
Sir why is b = 20?
The height of the cone is 20. If we let the side of the cone be represented by a straight line, and we position the x-y axis so that the y-axis goes through the center of the cone, then the y-intercept is at the top of the cone.
Doesn’t it say the radius is 20, not the height? On the board.
I would like to become u r student
From india
Impressive session
Thank you and welcome to the channel!
Hello Mr. Van Biezen,
You're videos have been a wonderful help and have greatly improved my grades. is there anyway to contact you by email?
thanks
You can send private messages via this channel on youtube, or you can simply send a message via this method and I will typically catch it.
You're showing too much of your back.