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As I am applying for an internship in research labs writing a cover letter is the most important part while applying.
I have gone through many websites regarding this, but I can't find the perfect way to write it.
Can you explain to me how to write a good cover letter?
Academic results and extracurricular activities should be shown in your resume/CV or on an application form if provided. It would be worth considering whether the extracurricular activities are relevant or demonstrate transferrable skills - they can be omitted if not. If the results are there, including them in the cover letter would be repetition, and if not it wouldn't help - the cover letter is not the place for these.
You can mention other work the professor has done, but I would be careful with this. If the work is relevant to the work you'll be doing, certainly mention it. If not, it could look obsequious and an overly flattering cover letter would be worse than no cover letter at all. (Not always the case - some professors might like this, but they're probably not the professors with whom you want to work.)
Cover letters are important, but a bad cover letter could adversely affect an applicant with even a perfect resume/CV. Bear in mind that the professor will be reading a lot of these, so while you'll want to stand out from other applicants, a multi-page letter would be a bad idea.
As with a lot of writing, the crux of this is to consider the audience. A good professor will want to know who you are and what interests you about the work you're hoping to do. That's all a good cover letter needs to show.
Speaking as both a professor and corporate division manager at different points in my life: Your cover letter is not your CV, and (as said by ItWasLikeThat) you should not try to cram your CV into it. The cover letter is more of a polite marketing tool to convince the professor you are the one for the job.
So I am interested in a brief summary of your experience and education, your GPA, courses you took specifically related to MY project / business.
More importantly, why are you interested in MY project / business? (and incidentally, this will show me if you have done your homework to read anything about me and my project / business).
Related, what do you hope to learn working on MY project?
I have to reject applicants; and although your CV will play a factor, your cover letter should be telling me why you should be on the short list. I would rather have an intern interested in my project and wanting to help it succeed than an intern that spends every minute alone staring into their phone and typing to their friends.
Obviously it must be short, you must mix relevant experience with your motivation to contribute tangible results and learn what the internship is supposed to provide to both of us; practical (i.e. real life) work experience for you, in exchange for relief of some novice-level workload for me.
If possible I will choose an intern with actual interest in my field; and that will override some CV hiccups (like your 'C' in art history) and whether you are in a barbershop quartet, on the soccer team, President of the Student Council or volunteer at the soup kitchen.
It depends on the professor’s subject, show the professor how reliable you are for the internship - in your letter, be precise and relevant. To your own accedmics and activities, they might prove you have experience.
