A sphere consists of a solid wooden ball of uniform density 800 kg/m^3 and radius .20 m and is covered with a thin coating of lead full with area density 20 kg/m^2.
A. calculate the moment of inertia of this sphere about an axis through the center.
For a sphere: I = (2/5)MR^2
Volume of a sphere: (4/3)pir^3
Area of a sphere: 4pir^2
D = m/v
The Attempt at a Solution
Ok, So this is what I did. I don't know the mass, so I have to find the mass through the density. So, for the uniform sphere itself, I did 800 kg/m^3 * (the volume of a sphere) and got the mass of the sphere without the lead covering to be 26.8083. Then I did the lead covering, I did 20 kg/m^2 * (volume of the sphere) and got 10.0531. So then, I added 26.8083 + 10.0531 and got 36.86. I then plugged this mass into the equation of inertia: I= (2/5)(36.86) (.20 (radius))^2 and got .590. However, that is not the answer. So if someone can tell me where I am going wrong, I would appreciate it. Thanks.