The volume of $1\textrm{ kg}$ of platinum is $(1000/21.45)\textrm{ cm}^3$, that is approximately $50\textrm{ cm}^3$. So $1$ tonne of platinum has an approximate volume of $50,000\textrm{ cm}^3$, or $1/20\textrm{ m}^3$. So about $5\textrm{ m}^3$ of platinum is produced per year, and so the total volume ever produced is $250\textrm{ m}^3%$. This is the same as a volume of a cuboid measuring $10\textrm{ m}\times5\textrm{ m}\times5\textrm{ m}$, which is similar to the size of a house.

*This problem is taken from the UKMT Mathematical Challenges.*