A sphere and a cube have same surface area. What is the ratio of the square of volume of the sphere to the square of volume of the cube? एक गोले और एक घन के पृष्ठीय क्षेत्रफल समान है । गोले के आयतन के वर्ग का घन के आयतन के वर्ग से क्या अनुपात है?

Let sphere radius = r and cube side = a. Surface area of sphere = 4πr², cube = 6a². Since equal: 4πr² = 6a², so r² = 3a²/(2π) and r = a√(3/(2π)). Volume of sphere = (4/3)πr³ = (4/3)πa³(3/(2π))^∕², cube = a³. Ratio of squares of volumes = [(4/3)πa³(3/(2π))^∕²]² : (a³)² = (16π/9)a⁶(3/(2π)) : a⁶ = (16π/9)(3/(2π)) = 8/3 = (6)/π.