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Question
A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of these balls are 1.5 cm and 2 cm. Find the radius of the third ball.
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Solution
Radius of sphere = 3 cm
Radius of first ball = 1.5 cm
Radius of second ball = 2 cm
Radius of second ball = 2 cm
`=4/3pixx3^3 -(4/3pixx3^3/2+4/3pixx2^3)`
`=4/3pixx3xx3xx3 - (4/3pixx3/2xx3/2xx3/2+4/3pixx2xx2xx2)`
`=4pixx3xx3-(pixx(3xx3)/2 + 4/3pixx2xx2xx2)`
`=36pi - (pi9/2+32/3pi)`
`=((36xx6-9xx3-32xx2)/6)pi `
`=((216-27-64)/6)pi =(125pi)/6`
Therefore,
`4/3pir^3 = (125pi)/6`
`Or, r = root(3)((125xx3)/(4xx6)) = root(3)(125/8) = 5/2 = 2.5 "cm"`
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