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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Calculus Problems, triple integral and polar coordinates stuff

**Physics Forums | Science Articles, Homework Help, Discussion**