A sphere whose volume is 16п is inscribed in a cube. find the volume of the cube.

The volume of the cube is calculated by the formula Vk = a ^ 3, where a is the side of the cube. Let R be the radius of the ball inscribed in the cube, then the side of the cube a = 2R.
The formula for the volume of a ball is Vs = 4/3 pi x R ^ 3.
It is known that Vs = 16 pi, i.e. 4/3 pi x R ^ 3 = 16 pi. Simplify the expression, divide the left and right sides of the equality by pi. We get 4/3 x R ^ 3 = 16, then R ^ 3 = 16/4 x 3 = 16 x 3/4 = 48/4 = 12.
Now we can calculate the volume of the cube Vk = a ^ 3 = (2R) ^ 3 = (2 ^ 3) x (R ^ 3) = 8 (R ^ 3) = 8 x 12 = 96.
Answer: the volume of the cube is 96.