surface areas of a sphere and cube are equal. then find the ratio of their volumes.
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SA of a sphere = 4πr²
SA of a cube = 6a²
4πr² = 6a²
r²/a² = 6 / 4π
(r/a)² = 3 / 2π
r/a = (3 / 2π)^0.5
Volume of a sphere = 4/3 πr³
Volume of a cube = a³
Ratio of their volumes = (4/3 πr³)/a³
= (4π/3)(r³/a³)
= (4π/3)(r/a)³
= (4π/3)(3 / 2π)^1.5
= (2²π/3)[3^1.5 / (2^1.5)(π^1.5)]
= √2√3 / √π
= √(6/π)
= 1.38 (Approx.)
SA of a cube = 6a²
4πr² = 6a²
r²/a² = 6 / 4π
(r/a)² = 3 / 2π
r/a = (3 / 2π)^0.5
Volume of a sphere = 4/3 πr³
Volume of a cube = a³
Ratio of their volumes = (4/3 πr³)/a³
= (4π/3)(r³/a³)
= (4π/3)(r/a)³
= (4π/3)(3 / 2π)^1.5
= (2²π/3)[3^1.5 / (2^1.5)(π^1.5)]
= √2√3 / √π
= √(6/π)
= 1.38 (Approx.)
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