Related Rates Worksheet
1. A piston is seated at the top of a cylindrical chamber with radius 5 cm when it starts moving into the
chamber at a constant speed of 3 cm/s. What is the rate of change of the volume of the cylinder when
the piston is 2 cm from the base of the chamber?
2. An angler hooks a trout and reels in his line at 4 in/s. Assume the tip of the fishing rod is 12 ft above
the water and directly above the angler, and the fish is pulled horizontally directly toward the angler.
Find the horizontal speed of the fish when it is 20 ft from the angler.
r
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ht) °
/ ,i sdecreasing a t I
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ftp.2Trhod#+iTr2dh- k i l l5 )2 h
i n d t V=25lTh
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* d¥=0becausetheradiusdoes netchangt
1 2 µft/s * 1 ¥ Given: §?,2{It do,¥=-4in/s=zft/s
2 0 f t dye0 LookingforD I d t d t202+122=2-2
2-2=544 x2+y2=z2 2=5544
z×d¥+2ydd¥=2Zdd¥
212074¥-121121107=25544/31 )
a¥=i¥¥%%9I#
3. Sand falls from an overhead bin and accumulates in a conical pile with a radius that is always three
times its height. Suppose the height of the pile increases at a rate of 2 cm/s when the pile is 12 cm
high. At what rate is the sand leaving the bin at that instant?
4. Two cylindrical swimming pools are being filled simultaneously at the same rate (in m 3 /min). The
smaller pool has a radius of 5 m, and the water level rises at a rate of 0.5 m/min. The larger pool has
-
Given: r - 3 h ¥=2cm/s when h=l2cm |¥§d¥=3§¥
V=§Tr2h. / \ 0 ¥
=3Th3
=-8641T-17281T ¥=9Th2dd¥
E.fi:37# ¥117119
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~ I - 8 - I 1 -5 - I
4=64114, r ,- 8 M
V I .25MHz dd¥=25Td± d t
DI-2511-10.5) a t dd¥=12 .5T⇒ sincet h epoolsa r ebeing
filleda t t h esamerate, dvftp.dydt-
d#=64iTdh1dt- 12.5iT=64iTdh1 dt da¥=, ¥gm1m§