1. The problem statement, all variables and given/known data Basically just to find moment of inertia of a spherical shell 2. Relevant equations Moment of Inertia = Int(r^2 dm) 3. The attempt at a solution I am in 12th grade and dont know much about integrals? Did I get lucky or am I right? I = Int(r^2dM) dM= (phi)(dA) I = Int(r^2 phi dA) Pull out phi, which equals M/4piR^2 I started by looking at half a sphere so I made that M/2piR^2. To get dA I figured you think of a bunch of hoops all going up to one point with a circumferance of 2piR, as you get higher up the radius changes however. A triangle says that R sin theta will get you the new radiuses, so for dA I wrote the integral of 2 pi R sin theta, dTheta. I put that in as dA, this R is a constant so now I have (M 2 pi R)/(2 pi R ^2) on the outside which cancels to M/R Now I have (M/R) Int(r^2 sin Theta, dTheta, dR) the R goes from 0 to R the theta from 0 to pi/2. The integral of sin Theta over that integral is 1, so it ends up (MR^3)/(3R) R's cancel MR^2/3 That's half a sphere so multiply by 2 2/3 M R^2 Was that luck or does that work?