How many balls with a diameter of 3 cm can be cast from a metal cube with an edge of 6 cm?

d = 3 cm.

a = 6 cm.

n -?

The number of balls n will be determined by the formula: n = Vcube / Vball, where Vcube is the volume of the cube, Vball is the volume of one ball.
The volume of a cube Vcube is determined by the formula: Vcube = a ^ 3, where a is the edge of the cube.
The volume of one ball Vball is determined by the formula: Vball = 4 * P * r ^ 3/3, where r is the radius of the ball, P is the number pi ..
r = d / 2.

Vball = 4 * P * d ^ 3/8 * 3 = P * d ^ 3/6.

n = 6 * a ^ 3 / n * d ^ 3.

n = 6 * (6 cm) ^ 3 / 3.14 * (3 cm) ^ 3 = 15.28.

Answer: you can pour n = 15 balls.