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Not Able To Obtain The Same Answer In Spherical/Cylindrical Coordinate

Hi,

I have to solve this problem using spherical coordinate and validate my answer using cylindrical coordinate, but I have 2 different answers, obviously!

Can anyone tell me what I am doing wrong? (See attached file for the problem and what I did)

Thanks, Mike.

EDIT: sorry, I used the wrong angle for the limit of , it should be not .

My new answer is 0,420894

EDIT 2: I drew the solid in my cad software and came up with a volume of 0,561.

I tried to do it the long way, calculating the volume of the cone, sphere and cylinder.

H of cone (z) =

Cone: V=

Sphere: V=

Cylinder: V=

Total volume = Cone + Cylinder - Sphere = 14.5104 - + 6.7343 = 4,48953

Since I only need from to (one eight) and not 2 , I divide by 8.

Re: Not Able To Obtain The Same Answer In Spherical/Cylindrical Coordinate

For the spherical coordinates case, your limits for look wrong. Firstly, if you're above the sphere, the lower limit should be 2. Secondly, you have not converted the Cartesian equation for the cone correctly into sphericals. The equation is a cone with vertex at the origin; this is not what you were given.