Measuring Cylindrical Luggage

Because of fit issues, the diameter would need to be less than the minimum dimension indicated. Another way to think about it is if you had a cardboard box the dimensions the airline gives, would your bag fit in it.

I like diameter by diameter by length. Will the bag be packed full or squishy?
In reality I have never seen airline personnel actually measure a bag. Usually there is a metal box and your bag must fit inside it. I have rarely seen that used either.

Cylindrical like a duffel bag? If it is a duffel, when packed, measure the length, its height, and its width at the widest part to verify it meets your airline's requirements. At the gate, the agent might instruct you to place it inside the template. If it fits, you're good to go.

There appears to be some misunderstanding that I do NOT intend to carry this on with me. I want to check it so here is the difference of what I am trying to understand:

How do the airlines measure cylindrical shaped luggage for baggage/cargo size limitations. Circumference X Length; Or: Diameter X 2 X length?
For example if I had a roll of drawings that stood 27 inches high if the circumfrence was used to calculate the maximum size limit of 62" then it could only be 11" in diameter because 11 X pie = 34.54 + 27 =   61.54  which is less than a total of 62 inches.

However if the measuring is based on the Height which would be the diameter, plus the width which would be the diameter again plus the length then the cylinder could have a diameter of:

27 - 62 = 35/2 = 17.5 inches which is significantly larger!
I don't believe they use a sizing frame for cargo bags which can include golf clubs, wheel chairs, hang gliders etc.
Thank you to all who respond(ed)!

I'd be extremely surprised if the airline did not use length + diameter + diameter. For a cylindrical object, that's the same as length + width + height, since measurements are normally taken at the widest point of each dimension.

Feel free to check a few airlines, but a quick check of Air Canada's rules says 'Linear Measurements ' The maximum linear dimensions of a piece of baggage are calculated by adding together its greatest outside height, width and length – wheels and handles included." So if it is cylindrical, then Diameter X 2 X length. This gives the overall measurement for consideration of whether it meets normal checked criteria (Air Canada is 62 inches), or becomes oversized which may incur extra costs.

Here's a good reference site for many airlines - this one is for carry-on:
https://travel-made-simple.com/carry-on-size-chart/

You mentioned 62 inches, that corresponds with Delta's checked bag limit before oversize checked bag limits apply. Their website clearly states that it is Length + Width + Height, so in your example, if you had a cylinder 11" in Diameter by 27", that would be 11+11+27= 49, less than 62 by a good stretch. You could certainly call your airline to get an exact answer, but what I laid out is the simplest answer, expecting that gate agents (on their wages) are going to use Geometry to calculate a circle, trapezoid, or rhombus is a bit too much. A bit more information (checking bag, what airline, even where you are flying to) would have been helpful as all that makes a big difference in the answer.

Typical luggage size is the sum of the out to out dimensions of a rectangular box:
Length + Width + Height

In the case of of a cylindrical bag (assuming a handle doesn't protrude):
Length + Diameter + Diameter

Airlines typically have exceptions for special luggage like sporting gear. For example Delta allows:

Javelins / vaulting poles are allowed except for travel to/from/via
Dublin (DUB) or Amsterdam (AMS). There is no limit on the length of
the pole, but oversized baggage fees will be applied to poles
exceeding 80 linear inches (203 cm).

Ski and snowboard equipment are allowed as checked baggage. One
ski/pole bag or one snowboard bag and one boot bag is accepted per
person. The combined weight of the ski/snowboard bag and the boot bag
may not exceed 50 lbs. or excess weight charges will apply. Linear
dimensions may exceed 80 inches (203 cm) without excess size
charges. All standard baggage charges apply.

I guess I could point out the mistake in your example, when you calculate circumference you are adding all sides into the equation. The formula used by the airlines only takes into account two of the four sides (Height and width). If you were to use comparable logic then in the second example you would need to do 11+11+11+11+27= 71, adding in all four sides, which is incorrect per the airlines guidelines.

Why not call the airline you are planning to use and ask them?

The airline is going to know their policy better than any of us.