A sphere with a diameter length of 14 in. is inscribed in a regular hexahedron. Find the exact volume of the space inside the hexahedron but outside the sphere.
To find:
The exact volume of the space.
Formula used:
Volume of Hexahedron:
Where
Volume of Sphere:
Given:
A sphere with a diameter length of 14 in. is inscribed in a regular hexahedron. Find the exact volume of the space inside the hexahedron but outside the sphere.
Calculation:
The diameter of the sphere is
The radius of the of the sphere is,
A sphere with a diameter length of 14 in. is inscribed in a regular hexahedron, so the diameter of length is equal to the hexahedron each sides of the length.
That is the length of the each sides of the of the hexahedron is
Therefore, the exact volume of the space is,
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