A group of children are using a large air mattress as a boat in a pool. The dens

Question

A group of children are using a large air mattress as a boat in a pool. The density of the air in the boat is 1.6kg/m^3. The boat is a short cylinder with circle area of radius 1.4m, and the height of 0.3m.
A. Calculate the volume of the mattress.
B. Calculate the mass of the air in the mattress, then the weight of the air.
C. The mattress' weight without air is 6.0 times the weight of the air mattress. Calculate the total mattress weight.
D. Considering that the boat floats and displaces some water, calculate the colume of water that is displaced by the EMPTY boat.
E. The water weight is equal to the boat weight if the boat floats. Considering the water displaced in QuestionC, calculate the height of submersion of the boat. (Hint: Use boat area; V=Ah)

The answers are
a) V = 1.85m^3
b) W = 29N
c) W = 209N
d) V = .0207m^3
e) h = .0033m

How do you get those answers, though?

Thanks!

Explanation / Answer

A) (V = pi r^2 h = 1.847m^2) B) (m = ho V = 2.95kg) (W = mg = 28.96N ~ 29N) C) (W-a = 6a; herefore W = 7a = 203N) I don't understand how you got 209N there. D) (203N = ho_{water} g V; ; V= 0.0203m^3) E) (pi r^2h' = 0.0203; h' = 3.297 imes 10^{-3} m ~ 0.0033m)

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