The surface area of a sphere and a cube are equal. Prove that their volume are in the ratio 1:
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Step-by-step explanation:Surface area of sphere = 4πr²
Total surface area of cube = 6a² (where a is side of cube)
∴ 4πr² = 6a²
r²=6a²/4π
r = √3a²/√2π
r = a√3/√2π
Volume of sphere = 4πr³/3
Volume of cube = a³
Ratio of volumes = 4πr³/3 ÷ a³
=4π(a√3/√2π)³/3 ÷a³ (by putting r=a√3/√2π)
=(4π/3) a³ × (3/2π) × (√3/√2π) ÷ a³
= 2√3/√2π
= √2 × √3/√π = √6/√π
= 1 ÷ √π/√6
= 1 : √(π/6)
Therefore ratio of volume of sphere to volume of cube comes out to be 1 : √(π/6)
Hence proved Thank you
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