"The cook has a grill."
Translation:Il cuoco ha una griglia.
Actually there is nothing indicating that the cook is female. In that case the masculine form is the way to go. In translating this as "la cuoca", I'd expect it to be clear from the context and this is not the case (maybe the cook is a male). I think "il cuoco" is the correct answer here, otherwise all other sentences would need to accept the female form and this would give the incorrect idea that the 2 forms are interchangeable at will.