What is the smallest number of whole logs that can be used?

What is the smallest number of whole logs (ρ = 745 kg/m3, radius = 0.0875 m, length = 3.24 m) that can be used to build a raft that will carry four people, each of whom has a mass of 72.5 kg?

weight of four people = 72.5 * 9.81 * 4 = 2844.9N
weight of logs = n * pi * 0.0875^2 * 3.24 * 745 * 9.81 = 569.55n N
floatation
= weight of water displaced
= n * pi * 0.0875^2 * 3.24 * 1000 * 9.81
= 764.5 n
764.5 n = 569.55n + 2844.9
n = 14.59
15 logs can be used to build a raft that will carry four people.

Note: there is no factor of safety in this case, normally a factor of safety 2 should be built into it.
The logs are almost fully submerged in water.

Source(s): my brain (Prof TBT)

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