Can a sonogram tell you exactly what week of pregnancy you're in?

I'm 30 or 32 weeks pregnant and i just found the exact date of the first day of my last period. When the doctor first asked me i wasn't for sure so i just kinda guessed. I figured it out for sure a couple of hours ago though and it turned out i was about 2 to 3 weeks off. I should tell my doctor right? And could he do a sonogram/ultrasound to find out exactly what week i'm in?