Tying up logs An Investigation

This investigation involves tying up logs with rope and trying to find the ‘best’ i.e. uses least rope, way to tie up the logs depending on how many logs have to be grouped together. Rope Logs In each diagram find the length of rope needed to tie the logs together. [The logs are all identical and have a diameter of 1 foot] (i) (ii) Leave all your answers in terms of (iii) What length of rope would be needed for 5, 6 and 7 logs using the above arrangement?

A timber merchant is involved each day in tying up thousands of logs before transporting them and he needs to consider different arrangements for tying the logs. Consider each arrangement below and work out the length of rope needed to tie the logs. (v) 4 logs (iv) 3 logs (vi) 4 logs (vii) 5 logs

(viii) 5 logs (ix) 6 logs (x) 6 logs (xi) 6 logs So what is the best way of tying up (i) 2 logs (ii) 3 logs (iii) 4 logs (iv) 5 logs (v) 6 logs Investigate tying up logs for larger numbers of logs using different arrangements.

Solutions Question Solution (i) (vii) (ii) (viii) (iii) (ix) (iv) (x)