SOLUTION: 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

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

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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 = , the side of the cube
:
Find the hypotenuse (h) of one side
h^2 =
h^2 = 2 * 6
h =
:
Find the diagonal, distance between opposite corners of the cube, this is also the diameter of the sphere
;
d^2 =
d^2 = 6 + 12
d = , also the diameter,
:
The S.A. of sphere =
S.A. = ,
S.A. = 18pi or 56.55 sq/inches

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