volumes (1 Viewer)

[lovelyq00]

just a question that i cant seem to work out properly!!

by taking slices perpindicular to the axis of rotation, use the method of slicing to find the volume of the solid obtained by rotating the region enclosed between the curve y=4-x^2 and the lines x=2 and y=4 through one complete revolution about

c) the line x=2

and

d) the line y=4

help pleasee?

 

[Riviet]

c) Take slices perpendicular to x=2, ie horizontal slices so that each of their thickness is ∆y.
Now we find the approximate volume of each of these slices:
∆V= πr²∆y
=π(2-x)²∆y
=π[2-(4-y)^1/2]∆y

We're summing up all the slices from y=0 to y=4 so these will be your limits when integrating.

d) Since axis of rotation is y=4, we take vertical slices that are perpendicular to this axis of rotation with thickness ∆x.
So ∆V=πr²∆x
=π(4-y)²∆x
=π[4-(4-x²)]²∆x
=πx⁴∆x

We're summing up all the slices from x=0 to x=2 so these will be your limits.

Hope that helps.

 

[lovelyq00]

ohh thanks alot! i have so much trouble visualising..

 

[Riviet]

It always helps to draw a neat diagram.