Related Rates
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APCD CALCULUS: RELATED RATES
Worksheet to Accompany Exploration, Part 1
Directions: After completing the Exploration, answer the following additional questions. The
Exploration is needed to answer some of these questions.
1. “Fill” the tanks to a “Maximum Depth” of 9. Then answer the following questions.
a) What is the ratio of the volumes of tanks
A
and
B
?
b) What is the ratio of the times it takes to fill the two tanks in part (a)?
c) What is the ratio of the volumes of tanks
B
and
C
?
d) What is the ratio of the times it takes to fill the two tanks in part (c)?
e) What is the ratio of the volumes of tanks
C
and
D
?
f)
What is the ratio of the times it takes to fill the two tanks in part (e)?
2. Now “Fill” the tanks to a “Maximum Depth” of 6. Then repeat parts (a) – (f) in problem 1.
3. Explain why the corresponding ratios in problem 2 differ from those in problem 1.
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4. Consider a tank that is a circular cylinder with a diameter of 8 feet.
a) What is the volume if the tank is filled to a depth of 9 feet?
b) How does the time required to fill this cylinder compare with the four tanks in the
Exploration?
c) How long would it take to fill it to a depth of 9 feet if
3
20 ft /min
dV
dt
=
?
d) What is
dh
dt
for this tank?
e) Why is
dh
dt
for the cylinder the same as
dh
dt
for all the tanks when
h
=9feet?
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 Spring '08
 Grether
 Calculus, Addition, Ratio, Tank, College Entrance Examination Board, college entrance examination

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