Latest SSC Aptitude Question SOLUTION: A sphere of diameter ' x ' and right circular cylinder of heights ' x ' and right circular cone of height ' x ' are of equal volume . The radii are in the ratio ?

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(#M40155506) SSC Numerical Ability question mensuration Keep an EYE

A sphere of diameter ' x ' and right circular cylinder of heights ' x ' and right circular cone of height ' x ' are of equal volume . The radii are in the ratio ?

Asked In SSC DEBARSHI DALAI (8 years ago)

Solved Devendra Marghade Read Solution (1)

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Devendra Marghade  (8 years ago) Best Solution

Sqrt(3) : Sqrt(2) : Sqrt(6)

Diameter of Sphere=x, so Radius=x/2, Volume of Sphere=(4/3)*Pi*(x/2)^3=Pi*x^3/6 ---(i)
If radius of cylinder=r1, then Volume of cylinder=Pi*r1^2*h=Pi*r1^2*x ---(ii)
If radius of cone=r2, then Volume of cone=(1/3)*Pi*r2^2*h=(1/3)*Pi*r2^2*x=Pi*r2^2*x/3 ---(iii)

As Volumes of all the three are same, comparing (i) =(ii) =(iii)
So ,Pi*x^3/6= Pi*r1^2*x = Pi*r2^2*x/3
r1=x/Sqrt(6) and r2=x/Sqrt(2)
Hence Ratio of radii are (x/2) : [x/Sqrt(6)] : [x/Sqrt(2)] = Sqrt(3) : Sqrt(2) : Sqrt(6)

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