A sphere and a cube have the same surface.Show that the ratio of the volume of the sphere to that of the cube is √6 : √π.
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TSA of cube = 6x²
TSA of sphere = 4 πr²
6x² = 4πr²
x²/r² = 4π/6
x/r = 2√π / √6 .
Their ratios of volumes = x³ / 4/3 πr³
= 3/4π * ( 2√π)³/(√6 )³
= 3/4π ( 8π√π) / 6√6
= 3*2√π / 6√6
= √π : √6 .
TSA of sphere = 4 πr²
6x² = 4πr²
x²/r² = 4π/6
x/r = 2√π / √6 .
Their ratios of volumes = x³ / 4/3 πr³
= 3/4π * ( 2√π)³/(√6 )³
= 3/4π ( 8π√π) / 6√6
= 3*2√π / 6√6
= √π : √6 .
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