# Moment of inertia of sphere

I know that the moment of inertia of a sphere is $\frac{2}{5}mr^2$ but using the perpendicular axis theorem we can get that the $I_z=I_x+I_y$ and they are all equal in case of the sphere because of its symmetry, therefore $I = I + I$ and then $I=0$! Isn't that wrong?

• Perhaps this is better asked on the physics stack exchange – SvanN Aug 28 '17 at 7:40