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The sink in Jeannette's bathroom is dripping and she wants to determine how much water is being wasted, so she borrows a graduated cylinder and leaves it to catch the drips for 5 minutes. When she comes back, she finds that it has 15 milliliters of water. If she leaves a cup with a diameter of 5 centimeters and a height 15 centimeters, about how long will it take to completely fill? 

 

Note: One milliliter is equal to one cubic centimeter

 Oct 5, 2019
edited by hellospeedmind  Oct 5, 2019
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The sink in Jeannette's bathroom is dripping and she wants to determine how much water is being wasted, so she borrows a graduated cylinder and leaves it to catch the drips for 5 minutes. When she comes back, she finds that it has 15 milliliters of water. If she leaves a cup with a diameter of 5 centimeters and a height 15 centimeters, about how long will it take to completely fill? 

 

(Das Waschbecken in Jeannettes Badezimmer tropft und sie möchte herausfinden, wie viel Wasser verschwendet wird. Deshalb borgt sie sich einen Messzylinder und lässt ihn für 5 Minuten stehen, um die Tropfen aufzufangen. Als sie zurückkommt, stellt sie fest, dass es 15 Milliliter Wasser hat. Wenn sie eine Tasse mit einem Durchmesser von 5 Zentimetern und einer Höhe von 15 Zentimetern zurücklässt, wie lange wird es dauern, bis sie vollständig gefüllt ist?)

 

\(v=\frac{V}{t}\\ v=\frac{15ml}{5min}\times \frac{min}{60s}\\ v=0.05ml/s\)

 

\(V=v\cdot t\\ t=\frac{V}{v}\\ V=\frac{d^2\cdot \pi \cdot h}{4}=\frac{5^2cm^2\cdot \pi \cdot 15cm}{4}\times \frac{ml}{cm^3}=294.524ml\)

\(t=\frac{V}{v}=\frac{294.524ml}{0.05ml/s}\)

\(t=5890.486s\times\frac{h}{3600s}=1.63625h\\ \color{blue}t=1h\ 38min\ 10.5s\)

laugh  !

 Oct 5, 2019

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