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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.
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Solution
Radius of a solid sphere = R = 15 cm
∴ Volume of sphere melted = `4/3piR^3`
= `4/3 xx pi xx 15 xx 15 xx 15`
Radius of each cone recasted = r = 2.5 cm
Height of each cone recasted = h = 8 cm
∴ Volume of each one cone recasted = `1/3pir^2h`
= `1/3 xx pi xx 2.5 xx 2.5 xx 8`
∴ Number of cones recasted = `"Volume of sphere melted"/"Volume of each cone formed"`
= `(4/3 xx pi xx 15 xx 15 xx 15)/(1/3 xx pi xx 2.5 xx 2.5 xx 8)`
= 270
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