Can I observe more than half the surface area of a convex object in one view? In a court scene in a movie, an eyewitness reported that he had eye contact with "the whole bus" during an event. A lawyer challenged this statement, saying "you can only observe the side of the bus that is facing towards you, which can never exceed 50%". This got me thinking:
Is it true that one can never view more than half of the surface area of any convex 3D object at the same time (without using optical devices like mirrors)? My thought is yes, since if the object is complete (with no holes), if you have a tiny surface area facing one direction, there must be another surface facing the exact opposite direction. But I can't proof this idea beyond "intuitive".
Does the surface of the object also have to be continuous?

I'm assuming that by how much you can see of the object, you mean the maximum surface area projected onto a plane. In that case, 2D should suffice because you could always rotate or add depth to make a prism. 
Take an isosceles triangle, point down, projected down onto a line parallel to the opposite side (think of setting it on the "ground" and then flipping it exactly upside down). Fix the perimeter $P = 1$. Then let the length of the parallel side be $\ell$. The length of the sides of the triangle that are facing the line is then $1- \ell$ and the fraction facing the line is $\frac{1- \ell}{1}$. As you make $\ell$ smaller, you get closer and closer to $100%$% of the triangle being "seen" by the line. 
Replace the triangle with a cone and it still works. So for a really "sharp" cone, you can see almost $100%$% of it (if you're exactly facing the point).
