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Question

Three solid spheres of radii 3 cm,4 cm and 5 cm respectively are melted and converted into a single solid sphere. Find the radius of this sphere.

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Solution

Given R1=3 cm,R2=4 cm and R3=5 cm

Combined volume of three given sphere =43π[R31+R32+R33]

Let R be the radius of the sphere formed after melting the original three spheres. So,

43πR3=43π[33+43+53]R3=216R=3216=6 cm

So, the radius of the solid sphere formed is equal to 6 cm.

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