Two spheres of same metal weigh 1 kg and 7kg if radius of smaller is 3cm then find diameter of larger
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Given : Two spheres of the Same metal weigh 1 kg and 7 kg . The radius of the smaller sphere is 3 cm .
We know volume of sphere = 4 π r33 , So
Volume of small sphere ( With radius of 3 cm ) = 4 ×π ×333 = 4 ×π × 273 = 4 ×π ×9 =36 π cm3
Mass ( Weight ) of small sphere = 1 kg
We know : Density = MassVolume , So
Density of small sphere = 136 π kg/cm3
Then ,
Mass of new formed sphere = 1 + 7 = 8 kg
Let , Radius of new sphere = r , So volume of new sphere = 4 π r33
And
Density of new sphere = 84 π r33 = 2π r33 = 6π r3 kg/cm3
As here given : Both sphere formed by same metal so density will be same .
Therefore,
6π r3 = 136 π⇒6r3 = 136⇒r3 = 216⇒r3 = 63⇒r = 6
So,
Radius of new sphere = 6 cm ( Ans )
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