Raft for children

The buoyant force exerted by water on the logs must be able to support the weight of the children equal to

$2 x 534 = 1068 N$

The buoyant force is given by

$F = V g ( ρw - ρl )$

ρw = density of water = $1000 kg/m^3$

ρl = density of log = $800 kg/m^3$

V = total volume of the logs = $\pi r^2 h n = \pi (0.15)^2 \times 1.8 n$

V = $0.1272 n$ , ( where n is the number of logs )

$1068 = 0.1272\times n \times g ( 1000 - 800 ) = 0.1272 n \times 9.8 \times 200$

n = 4.284

But you can not have logs in fraction so the required number of logs are $\lfloor{4.284}\rfloor$ = $5$

You need $\boxed{5}$ . Logs

$Weight\quad of\quad each\quad child\quad =\quad 534N\\ Weight\quad of\quad 2\quad children\quad =\quad 1068N\\ Let\quad the\quad no.\quad of\quad log\quad used\quad be\quad "n"\\ Radius\quad of\quad log\quad is\quad 0.15m\\ Volume\quad of\quad each\quad log\quad calculated\quad using\quad formula\quad \pi { r }^{ 2 }h\\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad =\quad 0.127\quad { m }^{ 3 }\\ Volume\quad of\quad "n"\quad logs\quad =\quad 0.127n\quad { m }^{ 3 }\\ Weight\quad of\quad each\quad log\quad calculated\quad using\quad formula\quad \rho V\\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad =\quad 997.5\quad N\quad \\ Weight\quad of\quad "n"\quad logs\quad =\quad 997.5n\quad N\\ Total\quad weight\quad of\quad the\quad system\quad (Children\quad +\quad Boat)\quad =\quad (1068\quad +\quad 997.5n)\quad N\\ Buoyant\quad force\quad =\quad weight\quad of\quad water\quad displaced\quad =\quad density\quad of\quad water\quad \times \quad Volume\quad of\quad water\quad displaced\quad \times \quad gravitational\quad acceleration\\ Volume\quad of\quad water\quad displaced\quad =\quad Volume\quad of\quad logs\quad (IN\quad THE\quad EXTREME\quad CONDITION)\\ Volume\quad of\quad "n"\quad logs\quad =0.127n\quad { m }^{ 3 }\\ Weight\quad of\quad water\quad displaced\quad =\quad 1000\quad \times \quad 0.127n\quad \times \quad 9.8\quad =\quad 1244.6n\quad N\quad =\quad Buoyant\quad force\\ Now\quad balancing\quad forces\quad on\quad the\quad system\\ 1244.6n\quad =\quad 1068\quad +\quad 997.5n\\ 247.1n\quad =\quad 1068\\ n\quad =\quad 4.4\\ Since\quad logs\quad cannot\quad be\quad a\quad fraction\quad we\quad have\quad to\quad use\quad 5\quad logs\quad to\quad make\quad the\quad boat\\ Because\quad the\quad density\quad of\quad log\quad is\quad less\quad than\quad the\quad density\quad of\quad water\quad so\quad we\quad have\quad to\quad increase\quad it\quad to\quad an\quad integer\quad rather\quad decreasing\quad it.$