Hi I have a homework set due this week, 14 problems, I have done 11 of them, but these 3 are giving me trouble, help would be great :)(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

1.A cylindrical drill with radius 4 is used to bore a hole through the center of a sphere of radius 8. Find the volume of the ring shaped solid that remains.

2.Use cylindrical coordinates to evaluate the triple integral [tex]\int\int\int_{E}[/tex] [tex]\sqrt{x^2+y^2}[/tex]dV , where E is the solid bounded by the circular paraboloid z=9−(x^2+y^2) and the xy -plane.

3.A volcano fills the volume between the graphs z=0 and z=[tex]\frac{1}{(x^2+y^2)^2}[/tex], and outside the cylinder x^2+y^2=1. Find the volume of this volcano.

3. The attempt at a solution

1. For the first one I know the volume of a sphere is 4/3[tex]\pi[/tex]r^3...so I found the volume and then I subtracted what I thought would be the volume of the cylinder, [tex]\pi[/tex]r^2h...for the height I used 16 because that's the diametre of the sphere sphere but I realized that the height of the cylinder will be a bit less but I can't figure out how much, and I would like to solve it with calculus too if I can but I can't figure out how to set up the integral.

2. For number two I have the integral as r^2dzdrd[tex]\theta[/tex], with the z limits 0 to 9-r^2, the r limits 0 to 3, and the [tex]\theta[/tex] limits 0 to [tex]\pi/2[/tex]...I am mainly uncertain about the [tex]\theta[/tex] limits, but am not sure about the others or the integral either. Is it right?

3. For the third I am not sure how to set up the integral, help please.

Thank you!

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# Calculus Problems, triple integral and polar coordinates stuff

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