SOLUTION: Hi! So i got a cylinder and in that cylinder there are 2 identical spheres they are touching themselves and the top and the bottom of the cylinder. The space that is left in t

Algebra ->  Bodies-in-space -> SOLUTION: Hi! So i got a cylinder and in that cylinder there are 2 identical spheres they are touching themselves and the top and the bottom of the cylinder. The space that is left in t      Log On


   

Question 551730:
Hi!
So i got a cylinder and in that cylinder there are 2 identical spheres they are touching themselves and the top and the bottom of the cylinder. The space that is left in the cylinder is 36pi. I need the r of the spheres

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Here is a central cross-section.  Each green and red line segment has
length r, the radius of each sphere and the cylinder:


The radius of each sphere and of the cylinder is r 

The height of the cylinder is 4r

Volume of the cylinder = pr²h = p(r)²(4r) = 4pr³


Volume of each sphere = 4%2F3pr³ 

Volume of cylinder - 2·volume of sphere = 36p

4pr³ - 2·4%2F3pr³ = 36p



4pr³ - 8%2F3pr³ = 36p

Multiply through by 3

12pr³ - 8pr³ = 108p

Divide through by p

12r³ - 8r³ = 108

       4r³ = 108

        r³ = 27

         r = 3

Edwin