Question

Find the volume inside the sphere defined by x^2+y^2+z^2=16 and outside the cylinder defined by x^2+y^2=4.

Answer 1

Would you check and see if you posted this part correctly: "cylinder defined by x^2+y^2=4"

This looks like a circle with radius 2.

Answer 2

sphere defined by x^2+y^2+z^2=16 --> we can get the volume of this; it is the cylinder that I am not understanding. @engineeringisharder

Answer 3

The cylinder is unbounded in the z direction making it a cylinder. however projected onto the xy plane it would be a circle. Since we are working in three dimensions then the naming of the object has to be there in order for this to work. It is a double integral over the region described by the two objects. So you would get a sphere with a cylinder cut out of the center with radius 2. Then we can integrate over the remaing region to find the volume.

Answer 4

I was trying to visualize the region described by the two functions. It gets tricky sometimes to get your bounds. That's the whole point of all of these sections that I am learning right now, it's tricky and confusing sometimes.

Answer 5

Thanks for the clarification. The "cylinder" term in the problem - would it be more accurately described as a "cylindrical surface?"