if a cube of maximum possible volume is cut off from a solid sphere of diameter D then the volume of the remaining waste material of the sphere would be equal to
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Solution:-
Diagonal of the cube =√3a²
= a√3
a√3 = d
a = d/√3
Volume of the sphere = 4/3 × π × (d/2)³
= 4/3 × π × d³/8
Volume of the sphere = 1/6 × π × d³
Volume of the cube = a³ = (d/√3)³ = d³/3√3
Volume of the remaining waste material = (1/6 × π × d³) - d³/3√3
= d³(1π/6 - 1/3√3)
Answer
Diagonal of the cube =√3a²
= a√3
a√3 = d
a = d/√3
Volume of the sphere = 4/3 × π × (d/2)³
= 4/3 × π × d³/8
Volume of the sphere = 1/6 × π × d³
Volume of the cube = a³ = (d/√3)³ = d³/3√3
Volume of the remaining waste material = (1/6 × π × d³) - d³/3√3
= d³(1π/6 - 1/3√3)
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