The volume of a cube is 8 cm3, find the square of its diagonal

univerkov | October 2, 2021 | education

For a cube, the lengths of all edges are equal, and its volume is equal to the cube of the length of its edges.

V = AA1 ^ 3 = 8 cm3.

Then AA1 = 3√8 = 2 cm.

Let’s construct the diagonal BD.

Triangle ABD is rectangular, then by the Pythagorean theorem, BD ^ 2 = AB ^ 2 + AD ^ 2 = 4 + 4 = 8.

ВD = √8 = 2 * √2 cm.

Triangular BB1D is rectangular, in which, according to the Pythagorean theorem, DB1 ^ 2 = BD ^ 2 + BB1 ^ 2 = 8 + 4 = 12 cm2.

Answer: The square of the diagonal of the cube is 12 cm2.

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