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Question
The surface area of a solid metallic sphere is 2464 cm2. It is melted and recast into solid right circular cones of radius 3.5 cm and height 7 cm. Calculate : the number of cones recast. `("Take" pi =22/7)`
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Solution
∴ R = 14 cm
Volume of sphere melted = `4/3 pi "R"^3`
`= 4/3 xx pi xx 14 xx 14 xx 14`
Radius of each cone recasted = r = 3.5 cm
Height of each cone recasted = h = 7 cm
∴ Volume of each cone recasted = `1/3 pi "r"^2"h"`
`= 1/3 xx pi xx 3.5 xx 3.5 xx 7`
∴ Number of cones recasted = `"Volume of sphere melted"/"Volume of each cone formed"`
`= (4/3 xx pi xx 14 xx 14 xx 14)/(1/3 xx pi xx 3.5 xx 3.5 xx 7)`
= 128
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