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    				| 1. | A cube of side 4cm contains a sphere touching itsside. Find the volume of the gap in between. | 
| Answer» Given,side of a cube = 4cm Side of cube = Diameter of sphere 4 = Diameter of sphere Radius of sphere = `(4)/(2)= 2 cm ` Volume of the gap = Volume of cube - Volume of sphere `= ("side")^(3) - (4)/(3)pir^(3)` `= (4)^(3) - (4)/(3) pi(2)^(2)" " [because "side of cube" = "diameter of sphere"]` ` = (64 - (4)/(3) xx (22)/(7) xx 8) = 64- 33.52 = 30.48cm^(3)` Hence, the volume of the gap in between a cube and a sphere is `30.48 cm^(3)`. | |