Thanks for the response! It's quite amazing that the centroid has this property. I may be overthinking it, but we are taking the product of a one and two dimensional object and getting a three dimensional result. Very cool!
@geraldglennmullet86654 жыл бұрын
A segment of a circle of radius R is bounded by an arc equal to 1/3 the circumference of the circle. Find the volume of the solid generated by revolving this segment about its chord as an axis. (This solid is know as Kepler's Lemon). Note: Do note use integral calculus.
@RaptrX11 жыл бұрын
You managed to do what my profesor couldn't in a full lesson. Thanks for clearing up some doubts that I had.
@ahmedsaeed65568 жыл бұрын
this video is not just helpful . it's helpful , great and awesome . actually you're doing great job . thanks for that inexpressible effort ..
@kristakingmath8 жыл бұрын
+ahmed saeed You're welcome, I'm happy to help!
@kristakingmath11 жыл бұрын
Think about the plane region, basically, a 2D triangle that sits inside the cone. The centroid of that triangle (basically the middle of it), will travel a distance when you revolve that triangle around the y-axis. That center dot will essentially form a circle when you rotate the region, and the circumference of that circle is the distance traveled by the centroid. I hope that makes sense!! :)
@miguelalvarado58248 жыл бұрын
Props young lady. Helped me with my Calc 2 homework, thanks!
@kristakingmath8 жыл бұрын
You're welcome, I'm so glad it helped! :)
@saidesmatullahhussaini93303 жыл бұрын
Best teacher ever
@kristakingmath3 жыл бұрын
Thank you so much!!
@jeffberhow11 жыл бұрын
What exactly does "distance traveled by the centroid of the plane region" mean; from where to where? Thanks for the great videos!
@kristakingmath11 жыл бұрын
Glad I could help! :)
@ptyptypty38 жыл бұрын
very WELL DONE, KRISTA!!.. You RULE.. :) ... by the way... a Great CHECK to see if your result is Correct.. (not that I think it wasn't correct!! ) .. is to Note that the Volume of a Cone is 1/3 the Volume of a CYLINDER using the same values for "h" and "r" .. and SURE ENOUGH.. you arrived at the 1/3(Pi)(r^2)(h) !!!! BINGO!! :) ... the area of the cylinder would be (Pi)(r^2)(h) !! THANK YOU KRISTA for all your wonderful AND very Educational Videos!! ..
@kristakingmath11 жыл бұрын
I didn't see VeryEvilPettingZoo's response before I responded. Thanks for helping each other... that's awesome!! :D
@husnainhyder67137 жыл бұрын
your method has helped me is there any method to analyze 3D problems. Thankyou
@Dewatch11111 жыл бұрын
could you not also find the equation of the line and rotate it around the y-axis by using it's bounds and the disk method? not positive if that would work but i feel like it could be a substitute
@rajeshagrawal46398 жыл бұрын
hey Krista I want to find center of mass of a rigid uniform body like that semi ring please help me out
@jaikhanna15329 жыл бұрын
when do we need the y coordinate..does the distance formula also change in that case?
@aubrey10083 жыл бұрын
Where does the 1/A come from. I don't get it. Can anyone explain?
@lyndongaming10 жыл бұрын
thanks, never understood any of what my professor explained for 2 hours. but in this video it took only around 10 mins
@kristakingmath10 жыл бұрын
So glad I could help simplify it for you! :)
@hg2.8 жыл бұрын
Yes L, Krista's videos give us "working knowledge"; a whole new generation of engineers is on the way, imho.
@husnainhyder67137 жыл бұрын
video is great but still have question about Y' is the formula of Y' is correct X' is verified from my side please help me with this matter
@kristakingmath11 жыл бұрын
Thanks! :)
@Neueregel11 жыл бұрын
Well done.
@chekurihrishikesh902210 жыл бұрын
Thanks .
@kristakingmath11 жыл бұрын
thanks!! :D
@amairanylopez47526 жыл бұрын
so simple! thank you!
@Boostedsoul7 жыл бұрын
hello can you state this theorem i mean statement of this theorem
@mannuposki109 жыл бұрын
I just had one doubt. Can you explain why did we consider only the x-coordinate and not y-coordinate?
@jasonlau15528 жыл бұрын
+Aman Sharma well if u are trying to find the distance of a straight line (which is in this case)u can neglect ur y corrdinate
@kunal_2658 жыл бұрын
Cos The triangle so form is rotating about y-axis, If it's rotating about x-axis, then we'll consider only y coordinate and not x centroid
@DaylightDigital10 жыл бұрын
I love this theorem!!!
@mayaachir13219 жыл бұрын
can somebody recap simply the problem for me plz ? it's for a project about Descartes for school...
@yopsi5224 жыл бұрын
when do you use this theorem on real life?
@rishirajdara11 жыл бұрын
I don't understand why the equation of F(x) is taken as the hypotenuse of the right angled triangle.
@gadddelarosa26925 жыл бұрын
Bcos it is the line that enclosed the cone and its equation is y=f(x)
@praveenkumarsunny915810 жыл бұрын
from where did u get the board and chalk on ur computer
@kristakingmath10 жыл бұрын
I explain here :) www.kristakingmath.com/my-videos
@Abc-tx4zr5 жыл бұрын
I don't understand why you can't just multiply 1/2 b (h)(2pi)(r)^2
@SAAD6385610 жыл бұрын
thank you
@kristakingmath10 жыл бұрын
You're welcome! :)
@adrieldelatorre62658 жыл бұрын
Thank you very much! :)
@kristakingmath8 жыл бұрын
You're welcome!
@adi87tya Жыл бұрын
If you're desi like me you can't stop giggling at "Pappu's theorem"
@matiaharonyan966310 жыл бұрын
inlove with you
@thomasfox98939 жыл бұрын
WTF is going on
@abochaser11 жыл бұрын
thanks a lot, but there was a mistake in your solution. after the integration, r cubed was changed to r squared. and with that being done, your result is wrong.
@Maddr3310 жыл бұрын
Yaarub Alanie it looks like the r's just canceled out. 1/3^r Xr^3
@abochaser10 жыл бұрын
oh ok. i am sorry. thanks again
@Maddr3310 жыл бұрын
I AM SO COOKED FROM FINALS THAT I tried and pick up my mouse and dial it.