Recasting


Sometimes, for various reasons, solid materials are melted and recast into other 3D solids. For example, a block of wax can be melted and recast to produce candles; a quantity of metal can be melted and recast to make metal components for cars or machinery; a sphere of plastic can be melted and recast to produce drinking bottles.


Whenever one solid is melted and recast as a new solid, the volume of the substance stays the same, assuming that none of the substance is lost in the process.


Volume of the original shape = volume of the new shape


To recast means to give a quantity of a substance a different form, by melting it down and reshaping it.


Worked example 2 A sphere made of wax with a radius of 15 cm is melted down and recast into a solid cube-shaped candle. Calculate the length of the edge of the cube to one decimal place. (Use π = 3⋅14 )


Solution


Practice questions 16.3


1. Lead spheres of diameter 6 cm are dropped into a cylindrical beaker containing some water and are fully submerged. The diameter of the beaker is 18 cm. (i) Calculate the volume of one sphere in terms of π . A number of these spheres are placed in the cylinder and the water rises by 40 cm. (ii) Calculate the number of spheres dropped into the cylinder.


2. A rectangular tray has length 60 cm, width 40 cm and depth 2 cm. It is full of water.


The water is poured into an empty cylinder of diameter 8 cm.


Calculate the depth, in cm, of water in the cylinder. Give your answer correct to three signifi cant fi gures.


264 Linking Thinking 2 40 cm 2 cm 60 cm 8 cm


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