Volumes by slicing (1 Viewer)

[.ben]

The area bounded by the curve y=x^3, y=8 and x-axis is rotated about the x-axis. Find the volume of the solid generated.

i just need to know what the shaded region looks like that's all. thanks

 

[Riviet]

If you sketch it on a number plane and shade it in 2D, it's just the shaded bit bounded by y=x³, y=8, the x-axis, plus this shaded region's reflection in the x-axis. Note that the area is not definite since there hasn't been an x boundary specified.

 

[SeDaTeD]

There isn't exactly an area that is 'bounded' by those three curves. It probably means the y-axis.

Oh and Riviet, what stops you from taking the rotation of the thing on the left side of y=x^3?

 

[Riviet]

Good point sedated, but now that I think about it, I'm confused as to which area it's referring to as well.

 

[SeDaTeD]

I'm quite certain you won't get asked to find volumes of unbounded regions in the HSC. Change x-axis to y-axis and it should be fine.

 

[.ben]

ok i'll try it.

i have another question: when you're taking cylindrical shells for an annulus, how do you know when to stop?

 

[Sober]

when you're taking cylindrical shells for an annulus, how do you know when to stop?

When your hand begins to hurt.














No seriously I have no idea what you are asking.

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