If Sum of volume of cone (A) and volume of cylinder (H) is 5040 π cm^3 and height of both cone and cylinder is same that is 20 cm and radius of cylinder is 12 cm, then what is the ratio of radius of A to radius of H.

Volume of cone = (1/3)πr_A²h and volume of cylinder = πr_H²h. Given total volume = 5040π, h = 20, and r_H = 12, we substitute: (1/3)πr_A²(20) + π(12)²(20) = 5040π. Simplifying gives (20/3)πr_A² + 1440π = 5040π, so (20/3)πr_A² = 3600π, giving r_A² = 540. Thus r_A = √540 = 6√15, and the ratio r_A : r_H = 6√15 : 12 = √15 : 2 = 3:2.