A ball is inscribed in the cube. Find the surface area of a cube if the total surface area of the ball is 149 n cm2.

The surface area of ​​a cube is equal to the sum of the areas of all its faces. Since the cube has six faces, the area formula looks like this:

S = 6a ^ 2.

Since the ball is inscribed in a cube, the diameter of this ball will be equal to the length of the face of this cube:

a = d.

Therefore, to calculate the area of ​​a cube, it is necessary to calculate the diameter of a given ball. To do this, apply the formula for the area of ​​a ball:

S = 4 π R ^ 2.

R2 = S / 4π;

R2 = 149π / 4π = 149/4 = 37.25;

R = √37.25 = 6.1 cm.

The diameter of the ball is equal to twice the radius:

d = 2R;

d = 6.1 * 2 = 12.2 cm.

Now we can find the surface area of ​​a cube:

S = 6 * 12.22 = 6 * 148.84 = 893.04 cm2.

Answer: the surface area of ​​the cube is 893.04 cm2.