Hi

I've got a question about "volume of solid of revolutions". First of all, what the heck does it mean?? I have never come across something like it before

Secondly, how do you solve this question from my textbook:

1) Find the volume of the solid of revolution about the y axis between the curve y = 2x^2 + 1 and the line y=1.5

2) Find the volume formed when the area bounded by y = lnx, y = 0 and x = 2 is rotated about the y axis.

We haven't covered these topics yet in class. I absolutely blew my first test and assignment so I'm trying to get ahead in the holidays.

Thanks for your time!!!

It might be wiser to focus on extensively revising and consolidating the material you've already covered rather than trying to learn new material (which I assume builds on material you've already covered ......)

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On problem A, I would first express the function as a function of y. Then the forumla for the volume of a solid of revolution is given by , where a and b are the lower and upper limits respectively.

As for question two: Do you wish to find the volume of the outside or the inside of the function? If you want the inside volume (below the function) translate y=0 into a limit on the x-axis and use the revolution volume formula. Is you want the outside volume, translate x=2 to a y-axis limit and express y=ln x as a function of y. Then use the revolution volume formula.


I assume this is the way to go.