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The radii of the bases of …

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The radii of the bases of two right circular solid cones of same height r1 and r2 respectively . The cones are melted and recasted into a solid sphere of radius R. Show that the height of each cone is given by h = 4R^3/r1^3+r2^3

Posted by Santosh Lamani 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

Let h be the height of each cone. Then,
Sum of the volumes of two cones = Volume of the sphere
{tex}\Rightarrow{/tex}{tex}\frac { 1 } { 3 } \pi r _ { 1 } ^ { 2 } h + \frac { 1 } { 3 } \pi r _ { 2 } ^ { 2 } h = \frac { 4 } { 3 } \pi R ^ { 3 }{/tex}
{tex}\Rightarrow{/tex} {tex}\left( r _ { 1 } ^ { 2 } + r _ { 2 } ^ { 2 } \right) h = 4 R ^ { 3 }{/tex}
{tex}\Rightarrow{/tex} {tex}h = \frac { 4 R ^ { 3 } } { r _ { 1 } ^ { 2 } + r _ { 2 } ^ { 2 } }{/tex}

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