Let a cube ABCDA₁B₁C₁D₁ be given. All six faces of the cube are equal squares with a side length equal to the length of the cube edge. Let the length of the edge be x cm. From the problem statement it is known that the perimeter of the cube faces is 32 cm.Knowing that the side of the square is related to its perimeter by the formula P (ABCD) = 4 ∙ x, we compose the equation:
4 ∙ x = 32;
x = 32: 4;
x = 8 (cm) – the length of the edge of the cube.
Then the area of the cube face will be: S (ABCD) = x²; S (ABCD) = 8² = 64 (cm²). The surface area of the cube will be:
S = 6 ∙ S (АВСD) = 6 ∙ 64 = 384 (cm²).
The volume of the cube will be:
V = х³ = 8³ = 512 (cm³).
Answer: the surface area of the cube is 384 cm², and the volume of the cube is 512 cm³.
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