I got 1968km for the Moon's radius. Not sure if this is the answer though (there aren't answers, although Google says it's 1737km).
Not sure whether a question like this is assessable...? Only based on the first line of the question; 'Using your knowledge of solar eclipses...'
Thanks in advance
Interesting question! Personally, I would have had a go at using similar triangles. This method is definitely not assessable, but it's interesting, so let's give it a go.
Using the 'knowledge of solar eclipses', we know that the moon appears to JUST block out the sun. We can draw ourselves a diagram, which would look something like this.
Okay, so, we can quickly find the acute angle between the earth and the tangent lines. The 'opposite' side is 700,000km and the 'adjacent' side is 150,000,000km plus the radius (700,000km), giving us 150,700,000km. So,
So, theta is equal to 0.26614 degrees. Now, let's use the 'moon' triangle. The angle is the same, but the 'opposite' and 'adjacent' sides are different.
That's pretty close to the real value! However, DEFINITELY not assessable in Physics (but a good 2U maths question!).
Thinking of a Physics way is a bit trickier. In fact, I'm not 100% sure there is a better way. How did you do it? An answer of 1968km, in my opinion, is probably correct; it's very close to the real value, which would be unlikely if you had done something wrong!