The edge of a cube is 3 cm. Find the volume of a cube, the surface area of a cube.

For a cube, all the faces are squares, so the length, width and height are equal. The area of ​​a cube is calculated as follows:
V = a ^ 3, where a is the length of the edge.

Therefore, the area of ​​our cube will be equal to:
V = 3 ^ 3 = 27 (cm cubic)

The surface area of ​​a cube is the sum of the areas of all its faces. The cube has 6 faces with the same areas. Therefore, now it remains to find the area of ​​one face of the cube to find the surface of the cube. The face area of ​​a cube is the area of ​​a square, so it is equal to:
S face = a ^ 2, where a is the length of the side of the square.
S faces = 3 ^ 2 = 9 (cm square)

Therefore, the surface area of ​​the cube is:
S surface of a cube = 6 * S faces = 6 * 9 = 54 (cm square)

Answer: V = 27 cm cubic, S surface of a cube = 54 cm square.