Question 1104361
A sphere is just inclosed inside the right circular cylinder.
 If the volume of the gap between cylinder & sphere is 90 cm cube.
 Find the volume of the sphere.
:
cylinder vol  - sphere vol = 90
({{{pi*r^2*h}}}) - ({{{4/3}}}*{{{pi*r^3}}}) = 90
The radius of the base of the cylinder and the radius of the sphere are the same
The height of the cylinder = the diameter of the sphere or 2r
({{{pi*r^2*2r}}}) - ({{{4/3}}}*{{{pi*r^3}}}) = 90
({{{pi*2r^3}}}) - ({{{4/3}}}*{{{pi*r^3}}}) = 90
factor out {{{pi*r^3}}}
{{{pi*r^3}}}({{{2 - 4/3}}}) = 90
{{{pi*r^3}}}({{{2/3}}}) = 90
multiply both sides b6 3
{{{2*pi*r^3}}} = 270
divide both sides by 2
{{{pi*r^3}}} = 135
r = {{{3sqrt(135/pi)}}}
find the cube root
r = 3.5026 cm
:
Find the vol of the sphere
V = ({{{4/3}}}*{{{pi*3.5026^3}}}) 
V = 180 cu/cm
:
The vol of the cylinder will be 270 cu/cm, interesting relationship!
see if that checks out
{{{pi*3.5026^2*7.0052}}} = 269.99, pretty close