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Question
A metallic cone of base radius 2.1 cm and height 8.4 cm is melted and moulded into a sphere. The radius of the sphere is
Options
2.1 cm
1.05 cm
1.5 cm
2 cm
Solution
2 . 1 cm
Radius of cone = 2.1 cm
Height of cone = 8.4 cm
Volume of cone`= 1/3 pi"r"^2"h" = 1/3pi (2.1)^2xx8.4`
`"Volume of the sphere" = 4/3 pi"r"^3`
Therefore,
Volume of cone = Volume of sphere
`=> 1/3pixx(2.1)^2xx8.4=4/3pi"r"^3`
⇒ 4.41 × 8.4 = 4r3
⇒ 37.044 = 4r3
`=> "r"^3 = 37.044/4`
= r3 = (2.1)3
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