Final answer:
To calculate the mass of a brass sphere with a 4 cm radius, we first determine its volume using the formula V = 4/3 πr³ and then multiply it by the density of brass. The problem solving requires knowledge of the sphere's volume calculation and the application of the density formula in physics.
Step-by-step explanation:
The question involves determining the mass of a solid brass sphere with a known radius using the concepts of volume and density. In physics, density (ρ) is defined as mass (m) divided by volume (V), expressed as ρ = m/V. To find the mass, we need the volume of the sphere and the density of brass. The volume (V) of a sphere is calculated using the formula V = 4/3 πr³, where r is the radius. Once we have the volume, we then multiply it by the density of brass to find the mass.
For a sphere with a radius of 4 cm, we calculate the volume as V = 4/3 π(4 cm)³. The density of brass is typically around 8.47 g/cm³. Multiplying the volume by the density gives us the mass: m = density × volume. Remember to convert the volume from cm³ to the appropriate unit if necessary to match the unit of density.
Exact numerical calculations were not performed in this explanation as the provided reference does not include an exact density value for brass. However, the concept and the general approach to solving the problem are clear.