The axial cross-sectional area of the cube is 4√2. Find the complete surface of a cube whose

The axial cross-sectional area of the cube is 4√2. Find the complete surface of a cube whose edge is three times the edge of this cube.

Let the length of the edge of the cube be X cm.

Then the diagonal AC, according to the Pythagorean theorem, is equal to: AC ^ 2 = AD ^ 2 + CD ^ 2 = X ^ 2 + X ^ 2 = 2 * X ^ 2.

AC = X * √2 cm.

The cross-sectional area of the cube is a rectangle АА1С1С, then Ssec = АА1 * АС.

4 * √2 = X * X * √2.

X ^ 2 = 4.

X = 2 cm.

Then the length of the edge of the second where is 3 * 2 = 6 cm.

The total surface area of a cube is equal to six areas of one of its faces.

S = 6 * AD * AA1 = 6 * 6 * 6 = 216 cm2.

Answer: The total surface area of a cube is 216 cm2.