• Quite a lot. Exactly how big is a pound coin in meters? As far as I am aware, this is not exactly common knowledge
• Find the radius and height of a pound coin. For accuracy. Treat the coin as a square (since two adjacent coins will have a gap between them). Find the volume of the (square) coin. Find the volume of the pool. Divide the first by the second.
• Diameter: 22.5mm Thickness: 3.15mm stolen straight from wikipedia. Now the rest is hard. What's the mathematically best way to pack pound coins into a swmiming pool to get the most in? The answer is, I believe, no one knows. Suppose we do it in layers. There will be 634 layers and not quite enough to get another in. How many on each layer? I imagine a pattern where there is a 25m long row of pound coins. There will be 1111 along the row. Make a new row of pound coins but offset it so that each coin on the second row lies between the coins on the first row. There will be 1110 in that row. Now alternate these two types of rows. Each coin in the middle of the pool will be surrounded by six others on the same layer. The rows will be separated by 22.5*cos(30) = 19.49mm That allows for 615 rows. So ok, I now have 307 rows of 1110 and 308 rows of 1111 to make 682958 per layer. That makes £432,995,372 But the 615 rows only occupy a width of 11986.64 mm. There's 13.36mm left, which is at least big enough for four more vertical layers at the edge of the pool. The vertical layers of 2m x 25m will contain at least 51 rows of 1111 and 50 rows of 1110 making an an additional £112,161 for a grand total of £433,107,533 without room to put one more coin in. But, there is still some wasted space at the edges, so a new packing method could get even more in. An upper limit would be to melt down the coins. Each coin occupies 1,252.5 cubic mm. And there are 600,000,000,000 cubic mm in the pool. So that's around £479,042,000 !