Volume of Solid: Calculating Y=2-X^2 Rotated about Y=1

[aurao2003]

Homework Statement

hi
i can't seem to make head or tail of this question. here it goes;

find the volume of the solid generated by rotating the area enclosed by the curve y= 2-x^2 and the line y = 1, about y=1.

i am not sure how to start. can someone please explain?

thanks

Homework Equations

The Attempt at a Solution

 

[berkeman]

Homework Statement

hi
i can't seem to make head or tail of this question. here it goes;

find the volume of the solid generated by rotating the area enclosed by the curve y= 2-x^2 and the line y = 1, about y=1.

i am not sure how to start. can someone please explain?

thanks

Homework Equations

The Attempt at a Solution

Start by drawing the x-y graph that shows both of those lines. Then picture how the parabolic curve can form a solid 3-d volume when rotated about the line y=1.

BTW, this looks more like a calculus problem than pre-calculus... Do you want me to move this thread to Calculus & Beyond?

 

[{~}]

I would use a triple integral in cylindrical coordinates.

the area of integration is the area enclosed by y = 2 - x² and the line y = 1

the line y = 1 is going to become our new z-axis and the new equation for the surface in this translated coordinate system is

<< equation deleted by berkeman >>

the latex interpreter is glitching right now so I'll post my solution later.

 

[berkeman]

I would use a triple integral in cylindrical coordinates.

the area of integration is the area enclosed by y = 2 - x² and the line y = 1

the line y = 1 is going to become our new z-axis and the new equation for the surface in this translated coordinate system is

<< equation deleted by berkeman >>

the latex interpreter is glitching right now so I'll post my solution later.

No, you will not post your solution later. The original poster (OP) must do the bulk of the work -- that is in the PF Rules (see the link at the top of the page).

I've deleted the equation that you wrote -- it did too much of the OP's work for them. Let them make the next post to show us their work. After that, you can provide hints, ask probing questions, correct mistakes, etc. But please do not do the student's work for them. Thanks.

 

[aurao2003]

its okay to move it.

 

[{~}]

Sorry I just thought that if the poster was didn't realize this was a calculus problem they probably wouldn't figure out the integral on their own.

It took me years to get a handle on integrals and I did that mostly be seeing others work.

Wolfram Alpha is a great resource as well.

 

[{~}]

aurora your next step is to figure out the boundaries of integration

 

[Calrik]

aurora your next step is to figure out the boundaries of integration

Exactly she/he has everything they need, it just takes working out a limit that says that x is between a and b when y is ?

Basic laws of spheres or shapes and pi therefore.

The equation can be transformed into something that has only one answer.

Integrate between limits. Is that giving away too much?

 

[berkeman]

Integrate between limits. Is that giving away too much?

No, those kind of hints are fine. Let's see what the OP comes back with...

 

[Calrik]

No, those kind of hints are fine. Let's see what the OP comes back with...

Thanks berk. Just feeling my way.

 

[aurao2003]

apologies for any replies. in crazy exam mode. 8 papers in january! i will reply soonest. thanks for the hints.