```Question 551730
<pre>
Here is a central cross-section.  Each green and red line segment has
length r, the radius of each sphere and the cylinder:
{{{drawing(200,400,-1,1,-2,2,
rectangle(-1,-2,1,2),

green(line(0,2,0,1),line(0,0,0,-1)),red(line(0,1,0,0),line(0,-1,0,-2)),
green(line(-1,1,0,1),line(-1,-1,0,-1)),red(line(0,1,1,1),line(0,-1,1,-1)),

circle(0,1,1),circle(0,-1,1) )}}}

The radius of each sphere and of the cylinder is r

The height of the cylinder is 4r

Volume of the cylinder = <font face="symbol">p</font>r²h = <font face="symbol">p</font>(r)²(4r) = 4<font face="symbol">p</font>r³

Volume of each sphere = {{{4/3}}}<font face="symbol">p</font>r³

Volume of cylinder - 2·volume of sphere = 36<font face="symbol">p</font>

4<font face="symbol">p</font>r³ - 2·{{{4/3}}}<font face="symbol">p</font>r³ = 36<font face="symbol">p</font>

4<font face="symbol">p</font>r³ - {{{8/3}}}<font face="symbol">p</font>r³ = 36<font face="symbol">p</font>

Multiply through by 3

12<font face="symbol">p</font>r³ - 8<font face="symbol">p</font>r³ = 108<font face="symbol">p</font>

Divide through by <font face="symbol">p</font>

12r³ - 8r³ = 108

4r³ = 108

r³ = 27

r = 3

Edwin</pre>```