Sandy 'Potter'
A sphere pot with inner radius 30 cm has a certain amount of sand and clay (not mixed together). The sand from the pot is emptied in a conical pot of base radius 12 cm and height 15 cm. All the sand completely fills the this pot and there is no excess sand. If the entire amount of clay from the spherical pot fills a cubical box, with no excess clay remaining, what is the length of the side of the box.
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1 solution
The volume of the sphere is 4/3 pi r^3 = sand volume + Clay volume......(1) Volume of cone is 1/3 pi r^2 = sand volume.....(2) (1)-(2)= clay volume = volume of cube Side of cube is cube root of this value = 48.03