The total surface area of a sphere and a cube is same .show that the ratio of there volume of the cube to that of sphere is√π: √6.
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Surface area of the sphere 4πr²
Surface area of the cube: 6x²
So according to the equation we get :
= 4πr² = 6x²
=> r²/x² = 6 / 4π
=> (r/x)² = 3 / 2π
=> r/x = (3 / 2π)^0.5
We know the volume of a sphere is 4/3 πr³ and Volume of a cube is: x³
we have to find the ratio so we can do : (4/3 πr³)/x³
=> (4π/3)(r³/x³)
=> (4π/3)(r/x)³
=> (4π/3)(3 / 2π)^1.5
=> (2²π/3)[3^1.5 / (2^1.5)(π^1.5)]
=> √2√3 / √π
=> √(6/π)
(equal) 1.38
Surface area of the cube: 6x²
So according to the equation we get :
= 4πr² = 6x²
=> r²/x² = 6 / 4π
=> (r/x)² = 3 / 2π
=> r/x = (3 / 2π)^0.5
We know the volume of a sphere is 4/3 πr³ and Volume of a cube is: x³
we have to find the ratio so we can do : (4/3 πr³)/x³
=> (4π/3)(r³/x³)
=> (4π/3)(r/x)³
=> (4π/3)(3 / 2π)^1.5
=> (2²π/3)[3^1.5 / (2^1.5)(π^1.5)]
=> √2√3 / √π
=> √(6/π)
(equal) 1.38
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