# Question #c9625

Jan 31, 2015

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.

$1 f t = 0 , 305 m$
$1 f {t}^{2} = {0.305}^{2} = 0.0930 {m}^{2}$

The pressure goes up by $\approx 10 k N / {m}^{2}$ for every meter down.
($N$=Newton is the metrical measure for force)

Top of the cube
Is at $9 \cdot 0.305 m = 2.745 m$
this gives a pressure of $27.450 k N / {m}^{2}$
Multiply by area: $F = p \cdot A = 27.450 \cdot 0.093 = 2.554 k N$

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

$F = 2.554 + 10.782 = 13.336 k N \approx 13.3 k N$
$13.3 k N = 618 l b$force.