Hello,
1) Use cylindrical coords to find the mass of the solid in the first octant inside the cylinder x^2 + y^2 = 4x, and under the sphere x^2 + y^2 + z^2 = 16, if the density equals the distance to the xy-plane.
The density is equal to the distance from the xy-plane, so I assume this means the density = z. The cylinder in the xy-plane should trace as a circle with radius 2 and centered at (2,0). This is where I get my limits of r=2 to r=4. Then, if I convert to polar, I end up with:
\(\displaystyle \int^{\frac{\pi}{2}}_{0}\int^{4}_{2}\int^{\sqrt{16-r^2}}_{0}} zr \ dzdrd\theta\)
This gives me an answer of 9pi.. but the correct answer should be 10pi. So close, but so far... Any idea where my error could be at? i've been over it again and again and can't find it.
1) Use cylindrical coords to find the mass of the solid in the first octant inside the cylinder x^2 + y^2 = 4x, and under the sphere x^2 + y^2 + z^2 = 16, if the density equals the distance to the xy-plane.
The density is equal to the distance from the xy-plane, so I assume this means the density = z. The cylinder in the xy-plane should trace as a circle with radius 2 and centered at (2,0). This is where I get my limits of r=2 to r=4. Then, if I convert to polar, I end up with:
\(\displaystyle \int^{\frac{\pi}{2}}_{0}\int^{4}_{2}\int^{\sqrt{16-r^2}}_{0}} zr \ dzdrd\theta\)
This gives me an answer of 9pi.. but the correct answer should be 10pi. So close, but so far... Any idea where my error could be at? i've been over it again and again and can't find it.