I sucked at geometry back in the day so I'm not standing on any sort of soap box but I don't think my method was wrong. To find the circumference of a circle, it's Pi * d. To turn that circumference into area (like you're extruding the circle upwards some dimension), you multiply C x H.
That would be the same if you had a line 10" long and then extruded it upwards 10" to create a plane that is 10 x 10 to get an area of 100 square inches. Roll that plane (sheet) into a cylinder with 10" circumference and 10" length.
The only time radius is invoked is when you need the area of a circle... which we don't care about in this case. I know it's included in formulas for volume of a cylinder. There are also formulas for surface area of a tube that can get you in trouble because it's accounting for the outer surface and inner surface.
That would be the same if you had a line 10" long and then extruded it upwards 10" to create a plane that is 10 x 10 to get an area of 100 square inches. Roll that plane (sheet) into a cylinder with 10" circumference and 10" length.
The only time radius is invoked is when you need the area of a circle... which we don't care about in this case. I know it's included in formulas for volume of a cylinder. There are also formulas for surface area of a tube that can get you in trouble because it's accounting for the outer surface and inner surface.