Climbing St Paul’s Cathedral

Here's a stimulus for a brief question, perhaps useful for Core Maths.

What can we do with this?

To start with we could look at the link between the height and the number of steps:

Gallery	Height in metres	Number of steps	Steps/metre	Height of each step (m)
Golden	85	550	6.47	0.155
Stone	53	398	7.51	0.133

It isn’t the same.  First thought is that the steps for the route up to the very top are about 2cm taller than the ones to the Stone Gallery.

But maybe it’s the same route, and everyone goes to the Stone Gallery first, with only some people going on the top.  In this case we need to find the difference in the height and in the number of steps:

Height in metres	Number of steps	Steps/metre	Height of each step (m)
32	152	4.75	0.211

These steps are considerably taller than the earlier ones (over 1 and a half times as tall).

The Shard in London is the tallest building in the EU at 309.6 metres.  It has a viewing gallery on the 72^nd floor (out of 95), which is 244.3 metres up.  Presumably people usually go via a lift, but there must also be emergency stairs.  How many stairs? 

Image from:

https://www.stpauls.co.uk/visits/visits/sightseeing-times-prices/new-sunday-dome-climb