A solid metal cylinder of radius 6 cm and height 10 cm is melted down. From the molten metal a solid cone of radius 9 cm and height 12 cm is cast, and every bit of the metal left over is used to make one solid sphere. Find the radius of that sphere in cm.

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Accepted Answer

3. Cylinder = π × 36 × 10 = 360π cm³. Cone = (1/3)π × 81 × 12 = 324π cm³. Metal left = 360π − 324π = 36π cm³. Setting (4/3)πr³ = 36π gives r³ = 27, so r = 3 cm.

A solid metal cylinder of radius 6 cm and height 10 cm is melted down. From the molten metal a solid cone of radius 9 cm and height 12 cm is cast, and every bit of the metal left over is used to make one solid sphere. Find the radius of that sphere in cm.

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