From a solid cube of side 7 cm, a conical cavity of height 7 cm and radius 3 cm is hollowed out. Find the volume of the remaining solid.


Since the conical cavity is hollowed out from the cube,


Volume of remaining solid = volume of cube - volume of cone


Now,


For Cube


Side, a = 7 cm


Volume of cube = (7)3 = 343 cm3


[ As Volume of cube = a3,


where a = side of cube]


For cone


Radius, r = 3 cm


Height, h = 7 cm


Volume of cone


[As volume of cone


where r = radius and h = height


Volume of remaining solid = 343 - 66 = 277 cm3


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