# Solid bounded by different region

In order to facilitate getting this thread finished I am including a picture:
View attachment 108270
This is looking almost straight down the z axis. You can see that the portion of the sphere inside the cylinder lies above the region which I will call ##D## which is the intersection of the two circles in the xy plane. So if you want the volume under the sphere and above the xy plane you have to set up the integral for the volume under the sphere over the region ##D## in polar coordinates. If you want to include the volume under the xy plane you would double that. That is what this problem is really about -- setting up that integral properly.
sorry , i really have problem understanding your diagram , can you explain further ? do you mean it's the view looking down from z a-xis ? if so , then i still cant understand it

In order to facilitate getting this thread finished I am including a picture:
View attachment 108270
This is looking almost straight down the z axis. You can see that the portion of the sphere inside the cylinder lies above the region which I will call ##D## which is the intersection of the two circles in the xy plane. So if you want the volume under the sphere and above the xy plane you have to set up the integral for the volume under the sphere over the region ##D## in polar coordinates. If you want to include the volume under the xy plane you would double that. That is what this problem is really about -- setting up that integral properly.
do you mean green part = sphere (x^2) + (y^2) + (z^2) = 9 ?
yellow part = (x^2) + (y^2) = 4x ??

But , why isnt the (x^2) + (y^2) = 4x closed ? it's a cylinder , right ?

In order to facilitate getting this thread finished I am including a picture:
View attachment 108270
This is looking almost straight down the z axis. You can see that the portion of the sphere inside the cylinder lies above the region which I will call ##D## which is the intersection of the two circles in the xy plane. So if you want the volume under the sphere and above the xy plane you have to set up the integral for the volume under the sphere over the region ##D## in polar coordinates. If you want to include the volume under the xy plane you would double that. That is what this problem is really about -- setting up that integral properly.
OK , but how do the solid formed look like ? I have problem of visualizing it . . . . . Can you sketch a separate diagram for the solid formed ?

Mark44
Mentor
do you mean green part = sphere (x^2) + (y^2) + (z^2) = 9 ?
yellow part = (x^2) + (y^2) = 4x ??
Yes, the green part is the upper half of the sphere,
But , why isnt the (x^2) + (y^2) = 4x closed ? it's a cylinder , right ?
It's a circular cylinder - the view, as LCKurtz said, is almost straight down the z-axis. The upper and lower ends of the cylinder are open, so I'm not sure what you're saying.

• Yes, the green part is the upper half of the sphere,
It's a circular cylinder - the view, as LCKurtz said, is almost straight down the z-axis. The upper and lower ends of the cylinder are open, so I'm not sure what you're saying.
Then the Object Formed Is A plane Instead Of solid? ? I Cant ImagIne Tge Solid Fomed

LCKurtz
Homework Helper
Gold Member
I think you need some face-to-face time with your teacher. I gather that English isn't your first language, but still, you don't seem to be understanding anything we are trying to tell you.

Mark44
Mentor
I think you need some face-to-face time with your teacher. I gather that English isn't your first language, but still, you don't seem to be understanding anything we are trying to tell you.
I agree completely. We are more than 30 posts into this problem, and you still don't understand what the solid looks like, despite multiple graphs and explanations from LCKurtz and me.

• I think you need some face-to-face time with your teacher. I gather that English isn't your first language, but still, you don't seem to be understanding anything we are trying to tell you.
sorry , after looking it carefully ,the solid formed is the red part ? (refer to the attachment)
So , the red part represent the projection to xy plane ?

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LCKurtz