# Science:Math Exam Resources/Courses/MATH101/April 2005/Question 05 (b)

MATH101 April 2005
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### Question 05 (b)

A water tank with depth 3 feet is in the shape of the trough depicted below. The bottom edge of the tank is 1 foot above the ground, and the ends of the tank are equilateral triangles of side length ${\displaystyle 2{\sqrt {3}}}$ feet; the top of the tank is a rectangle of length 12 feet and width ${\displaystyle 2{\sqrt {3}}}$ feet.

(b) Sometime after it is filled, the tank develops a small hole at its bottom. The tank then drains according to Toricelli's Law:

${\displaystyle A(y){\frac {dy}{dt}}=-k{\sqrt {y}},}$

where ${\displaystyle y}$ is the height of the water in the tank above its bottom, ${\displaystyle A(y)}$ is the area of the horizontal cross-section of the tank at height ${\displaystyle y}$, and ${\displaystyle k}$ is a positive constant. If the water level in the tank drops to 1 foot after 2 hours, how long will it take for the tank to empty?

(Do not simplify you answer.)

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