A solid hemisphere has radius 21 cm. It is melted to form a cylinder such that the ratio of its curved surface area to total surface area is 2 : 5. What is the radius (in cm) of its base (take π =22/7)

When a hemisphere is melted and recast into a cylinder, the volume remains constant. Volume of hemisphere = (2/3)πr³ = (2/3)π(21)³ = 2π(21)² × 7. For a cylinder with radius R and height h: πR²h = 2π(21)² × 7. The curved surface area (2πRh) to total surface area (2πR(R+h)) ratio is 2:5, giving h=R. This means R=21 cm from volume conservation.