The ratio between the total surface area of a solid right circular cylinder and a solid sphere is 2 : 1. If they have the same radii, the ratio of the volume of the cylinder to that of the sphere is given by - एक ठोस लम्ब वृत्तीय बेलन और एक गोले के कुल पृष्ठीय क्षेत्रफल में अनुपात 2 : 1 है। यदि उनकी त्रिज्यायें समान हैं, तो बेलन के आयतन का गोले के आयतन से अनुपात है-

For a cylinder with radius r and height h: total surface area = 2πr² + 2πrh, volume = πr²h. For a sphere with radius r: surface area = 4πr², volume = (4/3)πr³. Given surface area ratio = 2:1, we have (2πr² + 2πrh) / (4πr²) = 2/1. This simplifies to (2 + 2h/r) / 4 = 2, giving 2 + 2h/r = 8, so h/r = 3. The volume ratio = (πr²h) / ((4/3)πr³) = h / (4r/3) = 3h / 4r. Substituting h = 3r: volume ratio = 3(3r) / 4r = 9/4.