Answer:
The density of the steel sphere is approximately 9.59
Step-by-step explanation:
The parameters of the steel sphere are
The diameter of the sphere = 3.25 in.
The weight of the sphere, m = 3.21 lbs = 0.09976985 slug
The density of an object, ρ = (The mass of the object, m)/(The volume of the object, V)
The volume of a sphere, V = (4/3) × π·r³
Where;
V = The volume of the sphere
r = The radius of the sphere = (The diameter of the sphere)/2 = d/2
The radius of the given sphere, r = (3.25 in.)/2 = 1.625 in.
∴ The volume of the given sphere, V = (4/3) × π × 1.625³ = (2197/384)·π ≈ 17.974 in.³
The volume of the given sphere, V ≈ 17.974 in.³ ≈ 0.010401792195 ft.³
Therefore, the density of the steel sphere, ρ = m/V = (0.09976985 slug)/(0.010401792195 ft.³) ≈ 9.59 slugs/ft.³
The density of the steel sphere, ρ ≈ 9.59 slugs/ft.³