2016 AMC 12B Problema 11

The region sits below $y=\pi x;$ note $3\lt\pi\lt4,$ $6\lt2\pi\lt7,$ and $9\lt3\pi\lt10$

In each vertical strip $k\le x\le k+1,$ count the $1\times1,$ $2\times2,$ and $3\times3$ squares that fit below the line, then add them up

A square whose left edge is $x=k$ must fit below the lowest point of $y=\pi x$ over its width, namely $y=\pi k.$ For side length $1,$ the possible left edges $k=1,2,3,4$ contribute $3+6+9+12=30$ squares. For side length $2,$ the left edges $k=1,2,3$ contribute $2+5+8=15,$ and for side length $3,$ the left edges $k=1,2$ contribute $1+4=5.$ A square of side at least $4$ cannot fit, so the total is $30+15+5=50.$

Thus, the correct answer is D.