A Sphere And A Cube Have The Same Surface Area. Find The Ratio Of The

1.	A Sphere And A Cube Have The Same Surface Area. Find The Ratio Of Their Volumes?
Answer» SA of a SPHERE: 4πr² SA of a CUBE: 6x² 4πr² = 6x² r²/x² = 6 / 4π (r/x)² = 3 / 2π r/x = (3 / 2π)^0.5 Volume of a sphere: 4/3 πr³ Volume of a cube: x³ Find the ratio meaning (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). SA of a sphere: 4πr² SA of a cube: 6x² 4πr² = 6x² r²/x² = 6 / 4π (r/x)² = 3 / 2π r/x = (3 / 2π)^0.5 Volume of a sphere: 4/3 πr³ Volume of a cube: x³ Find the ratio meaning (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).

A Sphere And A Cube Have The Same Surface Area. Find The Ratio Of Their Volumes?

Answer»

SA of a SPHERE: 4πr²

SA of a CUBE: 6x²

4πr² = 6x²

r²/x² = 6 / 4π

(r/x)² = 3 / 2π

r/x = (3 / 2π)^0.5

Volume of a sphere: 4/3 πr³

Volume of a cube: x³

Find the ratio meaning (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).

SA of a sphere: 4πr²

SA of a cube: 6x²