Question 593550
A sphere is inscribed in a cube whose surface area is thirty six inches squared. Determine the surface area of the sphere.
 Determine the volume of the sphere
:
Let x = side of the square
S.A.: 6x^2 = 36
x^2 = 36/6
x^2 = 6
x = {{{sqrt(6)}}}, the side of the cube
:
Find the hypotenuse (h) of one side
h^2 = {{{2(sqrt(6))^2}}}
h^2 = 2 * 6
h = {{{sqrt(12)}}}
:
Find the diagonal, distance between opposite corners of the cube, this is also the diameter of the sphere
;
d^2 = {{{(sqrt(6))^2 + (sqrt(12))^2}}}
d^2 = 6 + 12
d = {{{sqrt(18)}}}, also the diameter,
:
The S.A. of sphere = {{{pi*d^2}}}
S.A. = {{{pi*(sqrt(18))^2}}}, 
S.A. = 18pi or 56.55 sq/inches