What is the volumetric capacity (in cubic cm) of a hexahedral cube whose diagonal measures 4√3 cm?
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Answer: D. 64
Explanation
The internal space diagonal of a hexahedral cube is calculated by multiplying its side length by the square root of three. Given a diagonal measurement of four times the square root of three, the side length a of the cube is four centimeters. The volumetric capacity of a cube is found by cubing its side length, giving four cubed which equals sixty four cubic centimeters. A hexahedral cube is a regular three dimensional geometric solid bounded by six identical square faces. The space diagonal connects opposite corners of a cube passing directly through its internal center point. Volume computation for cubes involves multiplying length, width, and height, which are all equal in a regular cube.
Eight underestimates the volumetric capacity by cubing two instead of the correct side length of four centimeters. Sixteen represents the squared area of a single square face rather than the total volumetric capacity of the cube. Twenty seven is incorrect because it assumes a side length of three centimeters instead of the derived value of four.
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- Mathematics
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