In general, when is it easier to measure the diameter of a circular object? When is it easier to measure the circumference?

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It is easier to find diameter of a circle when you know its radius ... recall the radius x 2 is the diameter.

Also, it is easier to find the circumference of a circle when you know it's diameter because circumference is defined by πd where d = diameter of the circle. These are of course indirect methods for measuring.