Volume with cross sections: semicircle | AP Calculus AB | Khan Academy

The volume of a solid with semi-circular cross sections and a triangular base.

AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.

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[TWPO]

Thank you, Sal. This was destroying my brain in class but you described it flawlessly

[chauphan]

I LIKE THIS VERY GOOD TEACHER. HIS WAY OF TEACHING IS VERY CLEAR.

[rabidpinkbunny]

THANK YOU. I feel like I understand this a lot better from watching this video than by staring at my textbook. XD

[TheKvacKaj]

Hello, I am not used to use integrals, but wouldn't it be easier in this case to solve it like this: 
We know that the radius of the base is 0, 5 and we also know that it's a semi cone. We can therefore apply volume of a cone formula divided by two: (pi*r^2*h)/6 (r=0, 5;h=1) and the result is pi/24 as we get from solving definite integral.

[danfow]

Was stuck on a Calc problem like normal. Thanks again Khan academy.

[IshowFUNNYvids]

God damn, I can't wait to learn Calculus!

[garyward]

x-1 looks like the radius of the half circle, not the diameter. please correct me if I'm wrong.  The volume of a cone formula, V=(1/3)x pi x r^2 x h, so cone with radius 1 and height of 1 has a volume of pi/3. The half cone volume would be pi/6. Please correct me if I am wrong.

[Lucuskane]

Move the constants, its not hard, but I have to remember that too often 

[garyward]

Sorry, meant to say 1-x, my point being that is the radius, not the diameter.

[TheJaguarthChannel]

I am sure that this is an extremely misshapen cone, and it breaks my brain when I try to fit the perfect half-cone he drew onto the graph he drew. Like, in side of the base of the cone must extend further than the other, due to the shape of the triangle that denoted the cross-section.

[TheKglennon]

Couldn't you solve this by using disk method and the Cavalieri theorem?

[aindoria]

You made this extra confusing for me because you added a perpendicular that didn't originally exist...