Latest SSC Aptitude Question SOLUTION: if the weight of a spherical shell is 7/8th of what it would be , if it were a solid shell . the ratio of inner radii is ?

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if the weight of a spherical shell is 7/8th of what it would be , if it were a solid shell . the ratio of inner radii is ?

Asked In SSC DEBARSHI DALAI (8 years ago)

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Rishu  (8 years ago)

1:2

let outer radius of the sphere be R and density be d
volume of solid sphere=(4/3)*pi*R^3
weight of solid sphere=[(4/3)*pi*R^3]*d

let inner radius of hollow sphere be r
volume of hollow sphere=(4/3)*pi*(R^3-r^3)
weight of hollow sphere=[(4/3)*pi*(R^3-r^3)]*d

according to question:
[(4/3)*pi*(R^3-r^3)]*d=(7/8)*[(4/3)*pi*R^3]*d
(R^3-r^3)=(7/8)*R^3
(1/8)*R^3=r^3
r^3/R^3=1/8
r/R=1/2
ratio of inner radius to outer radius=1:2

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