Maximum possible parts of a cake if cut n times In how many maximum/minium parts can a round cake($\large\text{ cylinder}$) be divided with $n$ cuts when each cut is necessarily a straight line? What would be the case if we have a circle,sphere,toroid,etc

This is known as the lazy caterer's sequence, the number is $\frac{n(n+1)+2}{2}$. The idea is to use Euler's Formula $E-V+F=2$ and the fact that the number of edges increases $1$ more than the number of vertices in each line.