A-rectangular-water-tank-is-being-filed-at-the-constant-rate-of-70lt-s-The-base-of-the-tank-has-width-w-9m-and-length-length-l-16m-if-the-volume-of-the-tank-is-v-w-l-h-where-h-is-the-hight-of-the-

Question Number 138217 by otchereabdullai@gmail.com last updated on 11/Apr/21

$$\mathrm{A}\:\mathrm{rectangular}\:\mathrm{water}\:\mathrm{tank}\:\mathrm{is}\:\mathrm{being}\:\mathrm{filed} \\ $$$$\mathrm{at}\:\mathrm{the}\:\mathrm{constant}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{70lt}/\mathrm{s}.\:\mathrm{The}\: \\ $$$$\mathrm{base}\:\:\mathrm{of}\:\mathrm{the}\:\mathrm{tank}\:\mathrm{has}\:\mathrm{width}\:\mathrm{w}=\mathrm{9m} \\ $$$$\mathrm{and}\:\mathrm{length}\:\mathrm{length}\:\mathrm{l}=\mathrm{16m}\:\mathrm{if}\:\mathrm{the}\:\mathrm{volume} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{tank}\:\mathrm{is}\:\mathrm{v}=\mathrm{w}×\mathrm{l}×\mathrm{h}\:\mathrm{where}\:\mathrm{h}\:\mathrm{is}\: \\ $$$$\mathrm{the}\:\mathrm{hight}\:\mathrm{of}\:\mathrm{the}\:\mathrm{tank}.\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{rate} \\ $$$$\mathrm{of}\:\mathrm{change}\:\mathrm{of}\:\mathrm{the}\:\mathrm{hight}\:\mathrm{of}\:\mathrm{water}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{tank} \\ $$

Commented by Dwaipayan Shikari last updated on 11/Apr/21

$${V}={wlh} \\ $$$$\Rightarrow\frac{{dV}}{{dt}}={wl}\frac{{dh}}{{dt}}\Rightarrow\mathrm{70}\frac{{litre}}{{s}}=\mathrm{160}{dcm}×\mathrm{90}\:{dcm}\frac{{dh}}{{dt}} \\ $$$$\frac{{dh}}{{dt}}=\frac{\mathrm{70}}{\mathrm{160}×\mathrm{90}}.\frac{{dm}}{{s}}=\frac{\mathrm{7}}{\mathrm{14400}}.\frac{{m}}{{s}} \\ $$

Commented by otchereabdullai@gmail.com last updated on 11/Apr/21

$$\mathrm{thank}\:\mathrm{you}\:\mathrm{sir}! \\ $$

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