Question

A sphere with radius 0.210 m has density rho that decreases with distance r from the center of the sphere according to rho=3.50��103kg/m3-(8.75��103kg/m4)r. What is the density of the sphere at a distance of 0.150 m from its center?

Answer 1

The density of the sphere at a distance of 0.150 m from its center is approximately 3.50 × 10^3 kg/m³.

Step-by-step explanation:

To find the density of the sphere at a distance of 0.150 m from its center, we can substitute the value of r into the given equation for density.

Given equation: rho = 3.50 × 10^3 kg/m³ - (8.75 × 10^3 kg/m⁴) * r

Substituting r = 0.150 m into the equation:

rho = 3.50 × 10^3 kg/m³ - (8.75 × 10^3 kg/m⁴) * 0.150 m

Calculating the density:

rho = 3.50 × 10^3 kg/m³ - (8.75 × 10^3 kg/m⁵)

rho = 3.50 × 10^3 kg/m³ - 1.3125 kg/m⁵

rho ≈ 3.50 × 10^3 kg/m³

The given density function for the sphere is ρ = 3.50 × 10^3 kg/m^3 - (8.75 × 10^3 kg/m^4) * r, where r is the distance from the center of the sphere. To find the density at a specific distance, substitute the given distance, r = 0.150 m, into the density function.

ρ(0.150) = 3.50 × 10^3 kg/m^3 - (8.75 × 10^3 kg/m^4) * 0.150 m

Calculate this expression to find the density at a distance of 0.150 m from the center. The result will be the density at that specific radial distance from the center of the sphere. The given formula suggests that the density decreases as the distance from the center increases, with a rate determined by the second term in the expression. This mathematical model allows you to understand how density varies with radial distance in the sphere.