The volume of the cube is equal to the volume of a parallelepiped with dimensions of 3 cm

The volume of the cube is equal to the volume of a parallelepiped with dimensions of 3 cm 4 cm 3 cm. Find the surface area of a cube.

1. Let’s find the volume of a rectangular parallelepiped if its length, height and width are 3 cm 4 cm 3 cm:

Vp = a * b * c;

Vp = 4 * 3 * 3 = 36 cm³;

2. According to the condition, the volume of the cube is equal to the volume of the parallelepiped, which means:

Vк = Vп = 36 cm³;

3. Knowing the volume of the cube, we find the length of the edge of the cube, if its volume is equal to Vк = а³:

a = ∛Vk;

a = ∛36;

4. Let’s find the area of the entire surface of the cube, if the area is equal to S = 6a²:

S = 6 * (∛36) ² = 6 * ∛36² = 6 * ∛36² = 6 * ∛6² * 6² = 6 * 6 * ∛6 = 36∛6.

Answer: the area of the entire surface of the cube is 36∛6.