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Question
What is the least number of solid metallic spheres, each of 6 cm diameter, that should be melted and recast to form a solid metal cone whose height is 45 cm and diameter 12 cm?
Solution
Let the number of solid metallic spheres be 'n'
Volume of 1 sphere
= `4/3pi(3)^3`
Volume of metallic cone
= `1/3pi6^2 xx 45`
`n = "Volume of metal cone"/"Volume of 1 sphere"`
`=> n = (1/3pi6^2 xx 45)/(4/3pi(3)^3)`
`=> n = (6 xx 6 xx 45)/(4 xx 3 xx 3 xx 3)`
`=>` n = 15
The least number of spheres needed to form the cone is 15
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