SOLUTION: one sphere is inscribed in a cube while the cube is inscribed in another sphere, what's the ratio of the volumes of the larger sphere to the smaller sphere.

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Question 982137: one sphere is inscribed in a cube while the cube is inscribed in another sphere, what's the ratio of the volumes of the larger sphere to the smaller sphere.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!

.
let rsdius of in sphere be r1 with volume v1
v1= 4/3 pi r1^3

radius of outer sphere = sqrt%282%29r1 (by Pythagoras theorem)
V2= 4/3 pi (sqrt(2))^3*r1


V2%2Fv1+=+%28%284%2F3%29+pi+%28sqrt%282%29%29%5E3%2Ar1%29%2F%28%284%2F3%29+pi+r1%5E3%29
)
v2/v1= 2sqrt%282%29%2F1