Platinum puzzle
What is the approximate total volume of platinum that has ever been produced?
Age
14 to 16
Challenge level
Problem
Platinum is a very rare metal, with a density of $21.5\textrm{ g/cm}^3$.
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
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: a house
Estimating using the total weight in grams
110 tonnes $\times$ 50 years = 5500 tonnes
= 5 500 000 kg
= 5 500 000 000 g
21.5 g $\approx$ 22 g (22 and 55 both multiples of 11)
5 500 000 000 $\div$ 22 = (55 $\div$ 22) $\times$ 100 000 000
= 2.5 $\times$ 100 000 000
= 250 000 000
The platinum occupies 250 000 000 cm$^3$ = 250 m$^3$
= 10 m $\times$ 5 m $\times$ 5 m
Estimating using the volume of 1 kg
21.5 g is approximately 1 cm$^3$
1000 g is approximately 1 cm$^3\times$50 = 50 cm$^3$
1000 kg is approximately 50 cm$^3\times$ 1000 = 50 000 cm$^3$
110 tonnes is approximately 50 000 cm$^3\times$ 110 = 5 500 000 cm$^3$
5 500 000 cm$^3$ = 5.5 m$^3$
So about 5.5 m$^3$ per year
5.5 m$^3\times$ 50 years $\approx$ 250 m$^3$
250 m$^3$ = 10 m $\times$ 5 m $\times$ 5 m