Find the area of a circle inscribed in one of the faces of a cube if the total surface area of the cube is 24.

The total surface area of a cube is equal to the sum of the areas of all its faces, and since the faces of the cube are equal to each other, then:

S = Sgr * 6;

Sgr = S / 6 = 24/6 = 4 – the area of one face of the cube.

The face of a cube is a square, the area of the face is equal to the square of the edge of the cube. Knowing the area of the face, we can find its side:

Sgr = a ^ 2;

a ^ 2 = √Sgr = √4 = 2 – the edge of the cube.

The diameter of a circle inscribed in a square is equal to the side of this square:

d = a = 2.

Therefore, the radius of this circle is: r = d / 2 = 2/2 = 1.

The area of a circle can be determined by the formula:

S circle = π * r2 = p.