Question #c9625

1 Answer
Jan 31, 2015

Answer:

618lbforce

Explanation:

The size of the pool is unimportant, as long as it can hold the cube. Only the depth matters, because this determines the pressure (=force per unit area).

It's a pity this problem was stated in old english measures.
I'll convert to metrical units, and convert the answer back.

#1ft=0,305 m#
#1ft^2=0.305^2=0.0930m^2#

The pressure goes up by #~~10kN//m^2# for every meter down.
(#N#=Newton is the metrical measure for force)

Top of the cube
Is at #9*0.305m=2.745m#
this gives a pressure of #27.450 kN//m^2#
Multiply by area: #F=p*A=27.450*0.093=2.554kN#

The sides
Since pressure rises linearly with depth, we may use the average pressure which will occur halfway up the cube.
Depth halfway is #9.5*0.305m=2.8975m#
Pressure will be #28.975kN//m^2#
Multiply by area: #28.975*4*0.093=10.782kN#

Answer
#F=2.554+10.782=13.336kN~~13.3kN#

Conversion:
#13.3kN=618lb#force.