Please help quickly!
A pool is in the shape of a cylinder, with a diameter of 16 meters, and a depth of 5 meters. A hose fills the pool up at a rate of 1 cubic meter every 5 minutes.

1.) After half an hour, what is the DEPTH of the pool?

2.) How much time (IN MINUTES) has passed when the pool is full?

Respuesta :

find the volume

volume=hpir^2
d/2=r=16/2=8


1.
hmm, ok, after 1/2 hour or 30 mins
30/5=6
6*1=6, 6 cubic meters
volume=6, solve for height
v=hpir^2
but r=8 all the time, solve for h
6=hpi8^2
6=hpi64
6/(64pi)=h
the depth is [tex]\frac{3}{32 \pi}[/tex] meters or about 0.02984155182973037545666570563235 meters
the depth is about 0.03 meters



2. the full volume is
v=6pi8^2=6pi64=384pi
1 cubic meter every 5 mins so
384pi/1 is how many 5 mininute intervals
so 384pi times 5=total minutes=1920pi minutes or about 6031.8578948924030178482752958966minutes
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