1. The problem statement, all variables and given/known data A cone has half angle θ0 and lateral surface area S0 in the frame in which the cone is at rest. If someone moves at relative speed β=v/c along the cones symmetry axis, what surface area will they see for the cone? 2. Relevant equations I believe the lateral surface area of a cone is S=πh2tanθ, where θ is the half angle and h is the height of the cone. Length contraction is also relevant; h1=h0√(1-β2) 3. The attempt at a solution S0 = πh02tanθ0 S1 = πh12tanθ1 If the cone had maximum radius R in the rest frame, it should remain R in the frame moving along the symmetry axis (because R is measured normal to this axis). So we have tanθ0=R/h0, and also tanθ1=R/h1, so we see tanθ1=(h0/h1)tanθ0 Putting all this together (with the length contraction relation) it seems to be that S1=S0√(1-β2) However my book claims S1=S0√(1-(βcosθ)2); so where is my mistake?