A solid cone with base radius 6 cm and height 8 cm is melted into a right circular cylinder. If the radius of the cylinder is half of the cone’s radius, what is its height?
Correct: A
Volume of the cone = (1/3)πr²h = (1/3)π(6²)(8) = 96π cm³. Let height of cylinder be H. Radius of cylinder = 3 cm (half of 6 cm). Volume of cylinder = π(3)²H = 9πH cm³. Equating volumes: 9πH = 96π ⇒ H = 96/9 = 32/3. Correct answer is closest option A.