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Question
A solid sphere of radius 15 cm is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate the number of cones recast.
Solution
For sphere, radius = R = 15 cm
For cone, radius = r = 2.5 cm, height, h = 8 cm
Let the number of cones recast be n.
∴ n x Volume of one cone = Volume of solid sphere
`=> n xx 1/3 pir^2h = 4/3piR^3`
`=> n xx (2.5)^2 xx (8) = 4 xx (15)^3`
`=> n = (4 xx 15 xx 15 xx 15)/(2.5 xx 2.5 xx 8)`
`=> n = 270`
Thus, 270 cones were recast.
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