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प्रश्न
A metallic solid right circular cone is of height 84 cm and the radius of its base is 21 cm. It is melted and recast into a solid sphere. Find the
diameter of the sphere.
उत्तर
We have,
Height of the cone, h = 84 cm and
Base radius of the cone, r = 21 cm
Let the radius of the solid sphere be R.
Now,
Volume of the solid sphere = Volume of the solid cone
`=> 4/3pi"R"^3 = 1/3pi"r"^2"h"`
`=> "R"^3 = ("r"^2"h")/4`
`=> "R"^3 = (21xx21xx84)/4`
`=>"R"^3 = 21xx21xx21`
`=>"R" = 21 "cm"`
∴ so, the diameter of the solid sphere is 42 cm.
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