Question

Use polar coordinates to find the volume of the given solid inside the sphere x^2+y^2+z^2=16 and outside the cylinder x^2+y^2=4

Answer 1

I need help with finding the limits I don't get why it's 2<=r<=4

Answer 2

the equations you have are sphere. right?

Answer 3

yes

Answer 4

well one of them is

Answer 5

ok so sphere has same radius.. its same like equation of circle. in that we had
x^2 +y^2 =r^2
means tthe part after equal is the radius.. and raidus is always constant.

Answer 6

okay so it's 4

Answer 7

and the cylinder is 2? but how do you know that the radius of the 2 has to be in between 2 and 4?

Answer 8

yes.. when you are working in 3D.. the second equation is also sphere but no direction in "z" thats all so you will treat the second one as sphere too

Answer 9

ok let me explain...

Answer 10

isn't the second one a cylinder?

Answer 11

yes its a cylinder.. sorry my bad.

Answer 12

you have tp find shaded part..
look the big circle have radius 4 and small cylinder has radius 2.. and u have to find the shaded part.

Answer 13

oh that makes a lot more sense, and it'd be 0 to 2pi right

Answer 14

awesome that was hard to see

Answer 15

yes if you are working in angle.. if you are working with raidus then 2 - > 4

Answer 16

lol ya i know.. i worked this stuff out last year.. nearly forgot how to do solving but lol still know how to imagine this stuff.

Answer 17

thanks so much for your help much appreciated!

Answer 18

you are most welcome ..