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During a chemistry lab, you use a funnel to pour slime into a flask. The radius of the funnel is 4 cm and the height is 12 cm. You pour the slime into the funnel at a rate of 60 mm per second and the slime flows out of the funnel at a rate of 40 mm per second. How long will it be before the funnel overflows with slime? Note: 1 mm is equal to 1 cubic centimeter. you do NOT need to do any conversions for this problem

 Jun 5, 2021
 #1
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Every second, 40 mm of slime exit the funnel, and 60 mm of slime enter the funnel.  In total, however, 20 mm of slime enter the funnel every second.  

 

If the radius of the funnel is 4cm and the height is 12 cm, assuming the funnel is cylinder-shaped, the volume should be \(4^2pi*12\) or 192 pi cubic centimeters.  Thus, the slime will overflow the funnel at 192pi/20 seconds into the initial pouring, or roughly 

 

30.1592894745 seconds into the experiment.  

 Jun 5, 2021

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