The diagonal of the cube is 7√3 cm. If the sphere inscribed inside is the largest possible sphere, what is the volume unoccupied by the sphere in the cube in cm³? (Take π = = ²/7)
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Step-by-step explanation:
Diagonal of Cube =a√3 units
7√3=a√3
Therefore a=7cm
Since largest possible sphere is inscribed in Cube
Diameter of sphere = Edge of cube
Therefore Diameter of cube=7 cm
Therefore Radius of cube=7/2 cm
For cube
l=7cm
For sphere
r=7/2 cm
Volume unoccupied by sphere= (Volume of cube) -(volume of largest possible sphere)
= l^3-4/3πr^3
=(7×7×7)-(4/3×22/7×7×7×7)
=490/3
=163.33 cubic cm
Therefore the volume unoccupied by the largest possible sphere in the given cube is 163.33 cubic cm
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