Question 287582
If a ball and a cube have the same volume, what is the ratio between the surface
 areas of the ball and the cube?
:
Choose a convenient value for the volume; 1000
then
side of cube = 10
S.A. = 6(10^2)
SA = 600 Sq/units; cube
:
Find the radius
{{{(4/3)pi*r^3}}} = 1000
multiply both sides by 3:
{{{4pi*r^3}}} = 3(1000)
r^3 = {{{3000/(4*pi)}}}
r = {{{238.732^(1/3)}}}
r = 6.2
Find the surface area
SA = {{{4*pi*6.2^2}}}
SA = 483.6 sq/units; sphere
:
Sphere/cube S.A. ratio: {{{483.6/600}}} ~ {{{4/5}}}