A bit more head scratching and they settled on the Airbus A380 as a unit of mass. Back to Google and Wikipedia and it turns out an Airbus A380 weighs in at 650 tonnes. That means the mountain of rice on the chess board has the same weight as 922 million Airbuses. It's still not easy to picture.

To make things easier we decided the height \(h\) of the mountain would be equal to the radius \(r\). That meant the cone/mountain volume was \(\tfrac{2\pi h^3}{3}\).

Plugging in the numbers and rearranging gave us a mountain height of 4,570 metres...give or take a bit.