The area of the diagonal section of the cube is 9 √2 cm2. Find the volume of a cube.

univerkov | July 27, 2021 | education

Let the length of the edge of the cube be equal to X cm, then, according to the Pythagorean theorem, the diagonal AC will be equal to: AC ^ 2 = AD ^ 2 + CD ^ 2 = 2 * X ^ 2.

AC = X * √2 cm.

The diagonal section of the cube is a rectangle АА1С1С.

Then Ssech = AC * AA1.

9 * √2 = X * √2 * X.

X ^ 2 = 9.

X = 3 cm.

Then the volume of the cube is: V = X3 = 27 cm3.

Answer: The volume of the cube is 27 cm3.

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