Graphing a Cylinder in R3

I

Idealistic

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Sep 7, 2007
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suppose -1 < y < 3

Then x[sup:2caucosk]2[/sup:2caucosk] + z[sup:2caucosk]2[/sup:2caucosk] - 4x - 2z + 1 = 0 represents a cylinder with a volume equal to 16pi?

A true or false question. I have:

(x - 2)[sup:2caucosk]2[/sup:2caucosk] +(z - 1)[sup:2caucosk]2[/sup:2caucosk] = 6

Does this yeild a circle wth a radius of (6)[sup:2caucosk]1/2[/sup:2caucosk] and a center of (2, 0, 1) (because y isn't a part of the equation above) or does -1 < y < 3 mean that this cylinder has a radius of (6)^[sup:2caucosk]1/2[/sup:2caucosk] and a height of 4, thus giving it a total volume of 8pi from (1/3)(pi)(6)[sup:2caucosk]2(1/2)[/sup:2caucosk](4)?

Either way question is false, but I have to justify my answer.

Thanks
 
Idealistic said:
suppose -1 < y < 3

Then x[sup:21jwx99b]2[/sup:21jwx99b] + z[sup:21jwx99b]2[/sup:21jwx99b] - 4x - 2z + 1 = 0 represents a cylinder with a volume equal to 16pi?

A true or false question. I have:

(x - 2)[sup:21jwx99b]2[/sup:21jwx99b] +(z - 1)[sup:21jwx99b]2[/sup:21jwx99b] = 6

Does this yeild a circle wth a radius of (6)[sup:21jwx99b]1/2[/sup:21jwx99b] and a center of (2, 0, 1) (because y isn't a part of the equation above) or does -1 < y < 3 mean that this cylinder has a radius of (6)^[sup:21jwx99b]1/2[/sup:21jwx99b] and a height of 4, thus giving it a total volume of 8pi from (1/3) (pi)(6)[sup:21jwx99b]2(1/2)[/sup:21jwx99b](4)?

Either way question is false, but I have to justify my answer.

Thanks
Click to expand...
Everything is correct except that (1/3) part.
 
Idealistic said:
oh so its not a circle? It's a cylinder with a volume of 24pi?
Click to expand...

It IS a circle.

The area of circle is = ? * r[sup:36sycpwz]2[/sup:36sycpwz]

Then multiply by height to get the volume of the cylinder.
 
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