when the beaker has rated capacity of 10 ml, does it mean that it has to be filled to the brim?

4 answers

No. Chemical beakers usually have an etched line in the glass where the liquid level is supposed to be when "full"
I didn't know that. I guess I always used "backward" beakers. Isn't technology great?
I answered based upon what I remember from college and high school chemistry. That was over 50 years ago. Apparently I was wrong.

There are such things as calibrated beakers. Some are shown at

http://www.alibaba.com/product-gs/51612146/glass_beaker.html

For info on the "rated capacity" of a beaker, see
http://www.apug.org/forums/forum37/6186-beaker-design.html
No, you probably are not wrong and I didn't doubt you. Your schools may have had the money to buy those calibrated beakers and mine didn't. Those calibrated beakers really are quite nice.