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Question
Three solid spheres of radii 3, 4 and 5 cm respectively are melted and converted into a single solid sphere. Find the radius of this sphere.
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Solution
Let R be the radius of single solid sphere.
Therefore,
Volume of single solid sphere = volume of all three spheres
`4/3 piR^3 = 4/3 pir_1^3 + 4/3 pir_2^3 + 4/3 pir_3^3`
`4/3 piR^3 = 4/3 pi (r_1^3 +r_2^3 + r_3^3)`
`R^3 = (3^3 + 4^3 + 5^3)`
`R^3 = 27 + 64 + 125`
`R^3 = 216`
`r = sqrt(216)`
` = 6`
`R = 6`
Hence, the radius of single solid sphere = 6 cm.
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