Children blinded a snowman, which traditionally consists of three snowballs, and 128 kg of snow went

Children blinded a snowman, which traditionally consists of three snowballs, and 128 kg of snow went to the lowest part with a radius of 46 cm, the diameter of each subsequent ball is the same number of times smaller than the previous one, only 2 kg of snow went to the snowman’s head. What is the height of the snowman?

Let m = 128 kg the mass of the first ball;
p is the density of snow;
V is the volume of the sphere;
R = 46 cm – radius of the first ball;
The volume of the ball is: V = (4/3) nR ^ 3;
m = p V;
128 = p * (4/3) * 3.14 * 46 ^ 3;
p = 128 / ((4/3) 3.14 46 ^ 3);
The radius of the second ball is n times smaller:
R2 = 46 / n;
R3 = 46 / (n ^ 2) – head radius;
The density of the snow, expressed in terms of R3, is equal to:
p = 2 / ((4/3) 3.14 (46 / (n ^ 2)) ^ 3);
Let’s equate the density:
128 / ((4/3) 3.14 46 ^ 3) = 2 / ((4/3) 3.14 (46 / (n ^ 2)) ^ 3);
64 = n ^ 6;
n = 2;
The diameter of the first ball is 46 * 2 = 92 cm;
The diameter of the second ball is 92/2 = 46 cm;
The diameter of the head is 46/2 = 23 cm;
The height of the snowman is: 92 + 46 + 23 = 161 cm.
Answer: 161 cm.