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Question
Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is ______.
Options
2 cm
3 cm
4 cm
6 cm
Solution
Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is 2 cm.
Explanation:
Let the diameter of each sphere be d cm.
Let r and R be the radii of the sphere and the cylinder, respectively, and h be the height of the cylinder.
As R = `"Diameter"/2.`
`"R" = 2/2 "cm" = 1 " cm"`
h = 16 cm
Therefore,
`=> 12 × 4/3xxpi"r"^3 = pi"R"^2"h"`
`=>12xx4/3"r"^3 = "R"^2"h"`
`=> 12xx4/3("d"/2)^3 = (1)^2 xx 16`
`=> 16xx"d"^3/8 = 16`
⇒ d3 = 8
⇒ d = ± 2
since d cannot of each sphere is 2 cm.
Hence, the diameter of each sphere is 2 cm.
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