Question

What mass of a material with density rho is required to make a hollow spherical shell having inner radius r1 and outer radius r2? (Use any variable or symbol stated above as necessary.)

Answer 1

Answer:

$\frac{4}{3}\rho\pi(r_2^3 - r_1^3)$

Explanation:

The volume of the shell is the difference between the volume of the outer sphere and the volume of the inner sphere

$V = V_o - V_i = \frac{4}{3}\pi r_2^3 - \frac{4}{3}\pi r_1^3$

$V = \frac{4}{3}\pi(r_2^3 - r_1^3)$

The mass of the shell is the product of the volume and its density

$m = V\rho = \frac{4}{3}\rho\pi(r_2^3 - r_1^3)$