Volume of a Cylinder: Find via Polar Graphs

[fonseh]

Homework Statement

Find the volume of solid bounded below by plane z = 0 , and above by z = 10 , sides by (x^2) + (y-1)^2 = 1 ..

Homework Equations

The Attempt at a Solution

I fins the area of the base first , which is pi (1^2) = pi , then i integrate with the length , which is from z = 0 to z=6 . so , my ans is 6pi , is my ans correct ?

But ,the author used cylindrical coordinate (polar graph method) , from r = 0 to r = 2sin theta , because the base of cylinder is centered at (0,1 )

 

[slider142]

Your problem statement says the cylinder lies between the planes z = 0 and z = 10, but your attempt at a solution uses only the interval from z = 0 to z = 6. Which one is correct?

 

[fonseh]

Your problem statement says the cylinder lies between the planes z = 0 and z = 10, but your attempt at a solution uses only the interval from z = 0 to z = 6. Which one is correct?

typo ,
I fins the area of the base first , which is pi (1^2) = pi , then i integrate with the length , which is from z = 0 to z=10 . so , my ans is 10pi , is my ans correct ?

But ,the author used cylindrical coordinate (polar graph method) , from r = 0 to r = 2sin theta , because the base of cylinder is centered at (0,1 )

 

[slider142]

That's fine. Your method is correct, and so is the author's. :-) I tend to prefer your method because its simpler. The author's intent is probably for you to compare the classical method to integration and see that they yield equivalent volumes for the classical solids.