Volume question - Method of slices (2 Viewers)

[ronnknee]

The arc of the curve y = cos x from x = 0 to x = pi / 2 is rotated about the y axis. Find the volume of the solid generated.

Okay, so when the cos x is rotated about the y axis, it would form a solid similar to a bell. If I take a horizontal slice of it, the radius would be x units. Therefore the area would be:

dV = pi x^2 dy

To make this work, we either change x in terms of y, but that would mean I'd have to integrate cos^-2 y, and I don't know how to do that. Another way I can think of is changing dy to dx, but how do I do that? Or is that wrong?

 

[ronnknee]

Ohh okay so I was on the right path all along
Thanks

 

[Iruka]

Have you learnt how to calculate volumes by shells?

http://www.mathlearning.net/learningtools/Volumes/unroller.html

Sometimes it is easier than using slices.

 

[jkwii]

but they will specify the method you have to use. of course shells is easier and the integration is ususally nicer but if they ask to do it by slicing in the hsc, you have to do it by slicing.

sorry

 

[Iruka]

but they will specify the method you have to use. of course shells is easier and the integration is ususally nicer but if they ask to do it by slicing in the hsc, you have to do it by slicing.

sorry

Of course, if they specify a particular method then you must use it. But the OP's question didn't specify a particular technique, which is why I suggested using shells.