- #1

andrew.c

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## Homework Statement

A rectandular swimming pool is 10m wide and 20m long. The bottom of the pools is a sloping plane with the depth of the pool varying along the length of the pool from 1m at the shallow end to 5m at the deep end. Water is being pumped into the pool at the rate of [tex]30 m^3 / min[/tex]. Shat that the total volume of water in the pook when the depth of thewater at the deep end is

*h*m (where [tex]0 \leq h \leq 4[/tex]) satisfies

[tex] V = 25h^2 [/tex]

Hence find the rate at which the water level is rising when the water is 3m deep at the deep end.

## Homework Equations

n/a

## The Attempt at a Solution

Equation to describe volume at h...

When 4m full, the 'length' filled by the water is 20m, therefore..

[tex]

\begin{align*}

V &= \frac{1}{2}LHW\\

&=\frac{1}{2}(5h)(h)(10)\\

&=(2.5h^2)(10)\\

&=25h^2\\

\end{align*}

[/tex]

Then, i tried to differentiate this expression to find h' (difference in height), but this came to 0.

Ideas?