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Question
A hollow metallic sphere with external diameter 8 cm and internal diameter 4 cm is melted and moulded into a cone of base radius 8 cm. The height of the cone is
Options
12 cm
14 cm
15 cm
18 cm
3 . 5 cm
Solution
External diameter = 8 cm
Internal diameter = 4 cm
Let the external and internal radii of the hollow metallic sphere be R and r, respectively.
Then,
External radius `8/2 = 4 "cm"`
Internal Radius = `4/2 = 2 "cm"`
Then, volume of the hollow sphere:
`4/3pi[("R")^3 - ("r")^3]`
`= 4/3 pi [(4)^3 - (2)^3]`
Therefore,
Volume of the hollow sphere
`4/3pi[(4)^3 - (2)^3] = 1/3pixx(8)^2 xx "h"`
`=> 4 (64-8) = 64 × "h" `
`=> 224 = 64 × "h" `
`=> "h" = 224/64`
⇒ h = 3.5 cm
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