半径 and 直径: from the center and across a circle
Distinguish radius from diameter and identify which length a stated measurement describes.
From the center to the circumference
半径, read はんけい, means radius. 半径三センチの円をコンパスで描きました。 reports drawing a circle with a three-centimeter radius using a compass.
Three centimeters measures from the center to a point on the circumference. It is not the diameter across the circle.
Across the center between opposite edges
直径, read ちょっけい, means diameter. この皿は直径が二十センチある。 gives this plate a diameter of twenty centimeters.
For a circle, diameter is twice radius. The three-centimeter-radius circle has a six-centimeter diameter; a twenty-centimeter-diameter circle has a ten-centimeter radius.
The basis of a drawing request
直径六センチの円を描いてください。 requests drawing a circle with a six-centimeter diameter. It does not request a six-centimeter distance between the compass center and its point.
When both measurements appear, identify their segments on the same circle. Do not confuse this length relationship with the entire circumference.
Is the diameter also three centimeters for a circle with a three-centimeter radius?
Show the answer and why
No. The diameter is six centimeters. Separate the center-to-circumference radius from the diameter across the center.