Mathematics

Mathematics

Problem

A solid metallic cone of base radius 6 cm6\,\text{cm} and height 18 cm18\,\text{cm} is completely melted. During melting, 5%5\% of the metal is lost. The remaining metal is recast into small solid cones, each having base radius 3 cm3\,\text{cm} and height 2 cm2\,\text{cm}. a. (i) Find the maximum number of small cones that can be obtained. b. (ii) Calculate the volume of metal left unused after casting these small cones (give your answer in cm3\text{cm}^3 to two decimal places).

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