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Two spheres of same metal weigh 1kg and 7kg. the radius of the smaller sphere is 3cm.the two spheres are melted to form a single big sphere. find the

diameter of the new sphere(board 2015-foreign)


Volume of smaller sphere = 4πr³/3 = 4π(3)³/3 = 36π cm³
∴ Density of this sphere, or metal,
= mass/volume
= (1000/36π) g/cm³

Both balls are made of same metal, hence they have equal densities.

∴ Volume of bigger sphere
= mass/density
= 7000/(1000/36π)
= (7*36
π) cm³

These two balls are merged i.e their volumes are added together.

∴ Volume of new sphere = 36π+(7*36π) = (36π*8) cm³
But, volume of new sphere = 4πr³/3

∴ 4πr³/3 = 36π*8
=> r³ = 9*8*3
=> r = ∛(3*3*3*8) = 3*2 = 6cm

Therefore radius of big cast sphere is 6cm.
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