Well, considering that we have a solid sphere and a spherical shell, it's time to juggle some numbers! Let's get cracking!
First, we need to calculate the volume of the solid sphere using its diameter. The formula for the volume of a sphere is V = (4/3) * π * r^3, where r is the radius. So, let's calculate the radius of the solid sphere first: r = diameter/2 = 5 cm / 2 = 2.5 cm. Now, we can calculate the volume of the solid sphere: V_solid = (4/3) * π * (2.5 cm)^3.
Next, we need to find the volume of the spherical shell. To do that, we'll subtract the volume of the inner sphere from the volume of the outer sphere. The radius of the outer sphere is half the external diameter: r_outer = 10 cm / 2 = 5 cm. The radius of the inner sphere is the radius of the outer sphere minus the thickness: r_inner = r_outer - thickness = 5 cm - 1 cm = 4 cm. Lastly, using the same formula, we can calculate the volumes: V_outer = (4/3) * π * (5 cm)^3 and V_inner = (4/3) * π * (4 cm)^3.
Now, to find the mass of the spherical shell, we subtract the mass of the solid sphere from the mass of the outer sphere:
Mass_shell = Mass_outer - Mass_inner
To get the masses, we use the formula Mass = Density * Volume. In this case, we know the mass of the solid sphere, so we can calculate the density using the formula:
Density = Mass_solid / Volume_solid
Therefore, the mass of the spherical shell is the density of the metal multiplied by the volume difference between the outer and inner spheres. Voila! You got yourself a solution!
Now, if only I knew the density of the metal you're talking about, we could take this mathematical circus to new heights!