Eight metallic balls of one centimetre radius each are melted into one ball. The diameter of the new ball is

To find the diameter of the new ball, we first calculate the total volume of the eight smaller metallic balls. The volume of a single sphere is given by the formula V = (4/3)πr³. Given each small ball has a radius (r) of 1 cm, the volume of one ball is (4/3)π(1)³ = (4/3)π cm³. Since there are eight such balls, their combined volume is 8 × (4/3)π = (32/3)π cm³. When melted into one large ball with radius R, its volume must equal this total: (4/3)πR³ = (32/3)π. Simplifying this equation, we find R³ = 8, which means R = 2 cm. The diameter of a sphere is twice its radius. Therefore, the diameter of the new ball is 2 × 2 cm = 4 cm.