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Question
A metallic spherical shell of internal and external diameters 4 cm and 8 cm, respectively, is melted and recast in the form of a cone of base diameter 8 cm. The height of the cone is ______.
Options
12 cm
14 cm
15 cm
8 cm
Solution
A metallic spherical shell of internal and external diameters 4 cm and 8 cm, respectively, is melted and recast in the form of a cone of base diameter 8 cm. The height of the cone is 14 cm.
Explanation:
Let the internal and external radii of the spherical shell be r and R, respectively.
Volume of the spherical shell`= 4/3pi("R"^3 - r^3)`
`=4/3 pi [(4)^3 - (2)^3] "cm"^3` .....[since` "r" ⇒ 4/2 = 2 " cm". "R"= 8/2 = 4 " cm"`]
`= (4/3pixx56) "cm"^3`
Radius of the cone `= 8/2 = 4 "cm"`
Volume of the cone `=1/3 pi"r"^2"h"`
Therefore
`1/3 pixx4xx4xx"h"xx = 4/3 pixx56`
`=> 16/3 xx "h" = 4/3pi xx 56`
`=> "h" = (4xx56xx3)/(3xx16)`
`=>"h" = 14 " cm"`
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