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:

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

Explanation:

• We have to make a hollow sphere of inner  radius $r_1$ and outer radius $r_2$.

Then the mass of the material required to make such a sphere would be calculated as:

Total volume of the spherical shell:

$V_t=\frac{4}{3} \pi.r_2^3$

And the volume of the hollow space in the sphere:

$V_h=\frac{4}{3} \pi.r_1^3$

Therefore the net volume of material required to make the sphere:

$V=V_t-V_h$

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

• Now let the density of the of the material be $\rho$.

Then the mass of the material used is:

$m=\rho.V$

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