A sphere with diameter 1 unit is enclosed in a cube of side 1 unit each. Find the unoccupied volume remaining inside the cube.
A sphere with diameter 1 unit is enclosed in a cube of side 1 unit each. Find the unoccupied volume remaining inside the cube.
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To find the unoccupied volume remaining inside the cube, we need to subtract the volume of the sphere from the total volume of the cube.
The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere. In this case, since the diameter is 1 unit, the radius would be 1/2 units.
The volume of the sphere is therefore V = (4/3)π(1/2)³ = (4/3)π(1/8) = π/6.
The volume of a cube is given by the formula V = side³. In this case, since the side is 1 unit, the volume of the cube is V = 1³ = 1.
Now, to find the unoccupied volume remaining inside the cube, we subtract the volume of the sphere from the volume of the cube.
Unoccupied volume = Volume of cube - Volume of sphere = 1 - π/6.
Thus, the unoccupied volume remaining inside the cube is 1 - π/6 units^3.