As you probably know, in the absence of air
resistance, all objects near the earth fall at the
same acceleration of 9.8 m/s2, no
matter their shape or size, and thus hit the
ground at the same time.
In the presence of air resistance, there is now an
upward force acting to slow down the objects as
they fall. In your question, you asked about cones
with 10 cm vs. 20 centimeter diameter. We need to
specify an additional assumption.
I will assume that the mass of the two cones is
the same. So, I´m imagining that you made two
different cones out of the same ball of clay, the
first one is taller and skinnier (10 cm diameter)
and the second one is shorter and fatter (20 cm
diameter). Now the main difference is the cross
sectional area of the falling object.
It´s the cross-sectional area (not the total
surface area) of the object which matters most in
a simple model of air resistance. The 20 cm
diameter cone will have a larger cross sectional
area, and will therefore fall slower.
You gave a falling distance of 2 meters. The
difference over this short of a fall may be very
difficult to measure, and the objects probably
won´t reach terminal velocity, but the answer and
the reasoning are the same no matter the length of