Mathematics: A rectangular tank that is 3 feet long, 6 feet wide, and 3 feet tall is filled with a liquid that has a density of p pounds per cubic foot. If a spout is connected to the top of the tank, how much work will it take to pump all of the liquid out of the tank through the spout

what diagram? you did not specify....

A rectangular tank that is 3 feet long, 6 feet

maddylife

23.01.2022

Therefore work required to pump out of all liquid is 81p ft-lb.

Step-by-step explanation:

Given that,

A rectangle tank dimension is 3 feet long, 6 feet wide and 3 feet tall.

The density of the liquid in the rectangular tank is p.

The volume of water $\triangle y$ of strip is

=long ×wide × $\triangle y$

=(3 ×6 × $\triangle y$ ) ft³

Force is = (3 ×6 × $\triangle y$ )×p pound

Total work done

$W=\int_0^3 3\times 6 \times p\times \triangle y(3- y)$

$=\int_0^318p (3- y)dy$

$=18p\int_0^3(3-y)dy$

$=18p[3y-\frac{y^2}{2}]_0^3$

$=18p[(3.3-\frac{3^2}{2})-(3.0-\frac{0^2}{2})]$

$=18p[9-\frac{9}{2}]$

$=18p\times \frac92$

=81p ft-lb

Therefore work required to pump out of all liquid is 81p ft-lb.

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