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