IMC 2005 Q17
17. Platinum is a very rare metal, even rarer than gold. Its density is 21.45 g/cm3. Assuming that the world production has been about 110 tonnes for each of the past 50 years, and negligible before that, which of the following has a comparable volume to that of the total amount of platinum ever produced?
- A a shoe box
- B a cupboard
- C a house
- D Buckingham Palace
- E the Grand Canyon
Intermediate Mathematical Challenge 2005, Question 17. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C a house
The volume of 1 kg of platinum is (1000/21.45) cm3, that is approximately 50 cm3. So 1 tonne of platinum has a volume of approximately 50 000 cm3, which is 1/20 m3. The volume of platinum produced per year is therefore about 5 m3 and the total volume of platinum ever produced is approximately 250 m3. This is the volume of a cuboid measuring 10 m × 5 m × 5 m, which is comparable to a house.
Solution © UK Mathematics Trust, from the IMC 2005 solutions.