Question

A sphere with radius 0.210 m has density rho that decreases with distance r from the center of the rho=3.25×10³ kg/m³−(9.50×10³ kg/m⁴)r. Calculate the total mass of the sphere. Express your answer with the appropriate units. X Incorrect; Try Again; 26 attempts remaining

Answer 1

To find the total mass of the sphere, we need to integrate the density function over the volume of the sphere.

Step-by-step explanation:

To calculate the total mass of the sphere, we need to integrate the density function over the volume of the sphere. The density function given is rho = 3.25×10³ kg/m³ − (9.50×10³ kg/m⁴)r, where r is the distance from the center of the sphere.

The volume of a sphere is given by V = 4/3 * π * r³. Substituting the density function in terms of r, we get the mass function as M(r) = (4/3 * π * r³) * (3.25×10³ kg/m³ − (9.50×10³ kg/m⁴)r).

To find the total mass of the sphere, we need to integrate the mass function over the entire volume of the sphere. The integral will be from 0 to the radius of the sphere.