A concrete ball weighs 0.5 tons. How many tons will a ball of twice the radius made of the same concrete weigh.

Let a given concrete ball, with a mass of m₁ = 0.5 t, have a radius of R₁ meters, then:

V₁ = 4 ∙ π ∙ R₁ ^ 3/3 (m ^ 3) – the volume of the first ball, where the coefficient π ≈ 3.14;

ρ = m₁: V₁ (kg / m ^ 3) is the density of the concrete from which the ball is made;

R₂ = 2 ∙ R₁ – the radius of the second ball is twice the radius;

V₂ = 4 ∙ π ∙ R₂ ^ 3/3 (m ^ 3) – the volume of the second ball;

m₂ = ρ ∙ V₂ = m₁: V₁ ∙ V₂ = (m₁: 4 ∙ π ∙ R₁ ^ 3/3) ∙ 4 ∙ π ∙ R₂ ^ 3/3 = (m₁: R₁ ^ 3) ∙ R₂ ^ 3 = (m₁ : R₁ ^ 3) ∙ (2 ∙ R₁) ^ 3 = 8 ∙ m₁ = 8 ∙ 0.5 = 4 (t) – weigh a ball of twice the radius, made of the same concrete.

Answer: A ball of twice the radius, made of the same concrete, will weigh 4 tons.