A right cylindrical upright tank of radius 20 cm is filled with water. If the tank is
being drained at 25 cubic cm per second, how fast does the height of water in the
tank drop?
Below is a correct solution to this problem. Next to each line, provide an explanation or reason of how it was derived.
dV
= −25 cubic cm per second
dt
dh
=?
dt
V = πr2 h
dr
dh
dV
= π2r h + πr2
dt
dt
dt
dV
dh
= 0 + πr2
dt
dt
−25 = π(20)2
dh
dt
−25
dh
=
= −0.02 cm per second
dt
π(20)2
State the final answer in one full sentence:
Write out in words and full sentences how you would explain to someone the process/steps by
which this problem is solved and what to look out for.