The radius of the Earth is 3.66 times the radius of the Moon; the average density of the Earth is 1.66

The radius of the Earth is 3.66 times the radius of the Moon; the average density of the Earth is 1.66 times that of the Moon. How many times is the body weight on the Moon less than on Earth?

Rzem / Rlun = 3.66.
ρzem / ρlun = 1.66.
Rzem / Rlun -?
Body weight is caused by the force of gravity. The weight of a body on earth Pzem is equal to the force with which the earth attracts this body Fzem.
Rzem = Fzem.
The weight of the body on the moon Rlun is equal to the force with which the moon attracts this body Flun.
Rlun = Flun.
The force of attraction of the body to the earth Fzem is determined by the formula: Fzem = G * mt * Mzem / Rzem ^ 2.
Where G is the gravitational constant, mt is the mass of the body, Mzem is the mass of the earth, Rzem is the radius of the earth.
The mass of the earth is determined by the formula: Mzem = ρzem * Vzem, where ρzem is the average density of the earth, Vzem is the volume of the earth.
The earth has the shape of a ball, therefore Vzem = 4 * п * Rzem ^ 3.
Fzem = G * mt * 4 * п * Rzem ^ 3 * ρzem / 3 * Rzem ^ 2 = G * mt * 4 * п * Rzem * ρzem / 3.
The force of attraction of the body to the moon Flun is determined by the formula: Flun = G * mt * Mlun / Rlun ^ 2.
Where G is the gravitational constant, mt is the mass of the body, Mlun is the mass of the moon, Rlun is the radius of the moon.
The mass of the moon is determined by the formula: Mlun = ρlun * Vlun, where ρlun is the average density of the moon, Vlun is the volume of the moon.
The moon has the shape of a ball, therefore Vlun = 4 * P * Rlun ^ 3.
Flun = G * mt * 4 * п * Rlun ^ 3 * ρlun / 3 * Rlun ^ 2 = G * mt * 4 * п * Rlun * ρlun / 3.
Rzem / Rlun = G * mt * 4 * п * Rzem * ρzem / 3: G * mt * 4 * п * Rlun * ρlun / 3 = Rzem * ρzem / Rlun * ρlun. = Rzem / * Rzem * ρzem / ρlun.
Rzem / Rlun = 3.66 * 1.66 = 6.
Answer: body weight on the ground is 6 times more than on the moon Pzem / Rlun = 6.