Solid o revol around x axis

[bradp]

my teacher told me that dr. bourell said there will be solids of revolution around the x-axis next year... did anyone else hear this?

and can't those easily be transformed into something that's around the y axis by changing the function? no special method needed?


edit grammre

[aalindsey100]

I heard something about that but I dont know much about solid of revolutions... I havent exactally made it to calculus yet... I know how to do them on my calculator... Ill have to ask my coach about that one...

This is really random but are you a senior this year?

[bradp]

junior

[ZachB]

For a solid of revolution around the x-axis, you just square the funtion, solve for the integral, and then multiply by pi at the end.

[Kurt]

I think my coach said he would start revolving around all sorts of other axes - not just the x-axis.

The method is the same...think about what you do when you revolve something around the y-axis:

Think of it as very small cylindrical shells added together. Each shell has a volume that can be approximated as [unparseable or potentially dangerous latex formula] (the circumference of the shell at that radius), times f(x) (the height), times dx (the width).

You could do the exact same thing around the x-axis by making it a function of y and using [unparseable or potentially dangerous latex formula] if you wanted to. Although you could just think of it now as adding together lots of "disks". Each disk has an area [unparseable or potentially dangerous latex formula] (since the function's value now becomes the radius sticking out of the x-axis)...in which case, the width is still dx.

You can do all sorts of methods like this to revolve around any axis pretty easily.

[bradp]