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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.)

Respuesta :

MechEngineer

Answer:

[tex]\frac{4}{3}\rho\pi(r_2^3 - r_1^3)[/tex]

Explanation:

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

[tex]V = V_o - V_i = \frac{4}{3}\pi r_2^3 - \frac{4}{3}\pi r_1^3[/tex]

[tex]V = \frac{4}{3}\pi(r_2^3 - r_1^3)[/tex]

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

[tex]m = V\rho = \frac{4}{3}\rho\pi(r_2^3 - r_1^3)[/tex]

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