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the largest possible sphere is carved out of a wooden solid cube of side 7 cm. find the volume of the wood left.
side of the cube = diameter of sphere = 7 cm
radius of sphere, r = (7/2) cm
Volume of wood left = Volume of cube - Volume of sphere           [vol. of cube = side3 , vol. of sphere = (4/3) pie r? 3 ]
= 7 * 7 * 7 - 4/3 * 22/7 * 7/2 *7/2 * 7/2
= 343 - 539/3
= (1029 - 539)/3
= 490/3
= 163.33 cu.cm


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