surface area of sphere and cube are equal.then find the ratio of their volume
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R = radius of sphere and length of edge of the cube = a
Surface area of sphere = surface area of cube
4 π R² = 6 a²
=> (R/a) = √3 / √2π
Volume of sphere / volume of cube
= (4π R³ /3) / (a³)
= 4π/3 * (R/a)³
= 4π/2 * [3√3 / (2 √2 π √π) ]
= 3 √3 /√(2π)
≈ 2.072
Surface area of sphere = surface area of cube
4 π R² = 6 a²
=> (R/a) = √3 / √2π
Volume of sphere / volume of cube
= (4π R³ /3) / (a³)
= 4π/3 * (R/a)³
= 4π/2 * [3√3 / (2 √2 π √π) ]
= 3 √3 /√(2π)
≈ 2.072
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