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Question
A hollow sphere of external and internal diameters 8 cm and 4 cm, respectively is melted into a solid cone of base diameter 8 cm. Find the height of the cone.
Solution
We have,
External radius of the hollow sphere, `"R"1 = 8/2 =4 "cm"`
Internal radius of the hollow sphere, `"R"2 = 4/2 = 2 "cm" and`
Let the height of the cone, `r = 8/2 = 4 "cm"`
Let the height of the cone be h.
Now, Volume of the cone = Volume of the hollow sphere
`=> 1/3pi"r"^2"h" = 4/3pi"R"_1^3 - 4/3pi"R"_2^3`
`=> 1/3pi"r"^2"h" = 4/3pi("R"_1^3 - "R"_2^3)`
`=> "h" = 4/"r"^2 ("R"_1^3 - "R"_2^3)`
`=> "h" = 4/(4xx4) (4^3 - 2^3)`
`=>"h" = 1/4(64-8)`
`=> "h" = 1/4xx56`
∴ h = 14 cm
So, the height of the cone is 14 cm.
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