How many grams of copper are required to make a hol-low spherical shell having an inner radius of 5.70 cmand an outer radius of 5.75 cm? The density of copperis 8.92 g/cm

To solve this problem, we need to find the volume of the copper used to make the spherical shell. The volume of a sphere is given by the formula 4/3πr³. The volume of the shell is the difference between the volume of the outer sphere and the volume of the inner sphere.

1. Calculate the volume of the outer sphere: V_outer = 4/3 * π * (5.75 cm)³

2. Calculate the volume of the inner sphere: V_inner = 4/3 * π * (5.70 cm)³

3. Subtract the volume of the inner sphere from the volume of the outer sphere to get the volume of the shell: V_shell = V_outer - V_inner

4. Multiply the volume of the shell by the density of copper to find the mass of the copper needed: mass = V_shell * density

Let's calculate:

1. V_outer = 4/3 * π * (5.75)³ = 795.21 cm³
2. V_inner = 4/3 * π * (5.70)³ = 777.22 cm³
3. V_shell = 795.21 cm³ - 777.22 cm³ = 17.99 cm³
4. mass = 17.99 cm³ * 8.92 g/cm³ = 160.45 g

So, approximately 160.45 grams of copper are required to make the hollow spherical shell.