The sum of the areas of the side faces of the cube is 216 cm2. find the length of the diagonal of the cube.
| March 3, 2021 | education
The cube has four side faces, then the area of one side face is:
Saa1v1v = Sside / 4 = 216/4 = 54 cm2.
Then the length of the edge of the square is √54 cm.
In a right-angled triangle ABC, according to the Pythagorean theorem, AC ^ 2 = AB ^ 2 + BC ^ 2 = 54 + 54 = 108.
In a right-angled triangle ACC1, according to the Pythagorean theorem, AC1 ^ 2 = AC ^ 2 + CC1 ^ 2 = 108 + 54 = 162.
AC1 = 9 * √2 cm.
If 216 cm2 is the total surface of the cube, then AC1 = 6 * √3 cm.
Answer: The length of the diagonal of the cube is 9 * √2 cm, (6 * √3) cm.
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