Three solid metallic spheres of radius 12 cm, 16 cm, and 20 cm are melted and recast into a new solid sphere. Find the diameter of the new sphere. 12सेमी , 16 सेमी एवं 20 सेमी त्रिज्या वाले गोलो को गलाया गया एवं नया गोला बनाया गया। नये गोले की त्रिज्या ज्ञात कीजिए।

Volume is conserved when melting and recasting. Total volume = (4/3)π(12³ + 16³ + 20³) = (4/3)π(1728 + 4096 + 8000) = (4/3)π(13824). For the new sphere with radius R: (4/3)πR³ = (4/3)π(13824), so R³ = 13824 = 24³. Therefore, R = 24 cm. (Note: The English text asks for 'diameter' but Hindi asks for 'त्रिज्या' (radius); the answer 24 cm refers to the radius).