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

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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) About Me  (Show Source):
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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%286%29, the side of the cube
:
Find the hypotenuse (h) of one side
h^2 = 2%28sqrt%286%29%29%5E2
h^2 = 2 * 6
h = sqrt%2812%29
:
Find the diagonal, distance between opposite corners of the cube, this is also the diameter of the sphere
;
d^2 = %28sqrt%286%29%29%5E2+%2B+%28sqrt%2812%29%29%5E2
d^2 = 6 + 12
d = sqrt%2818%29, also the diameter,
:
The S.A. of sphere = pi%2Ad%5E2
S.A. = pi%2A%28sqrt%2818%29%29%5E2,
S.A. = 18pi or 56.55 sq/inches