JName
Date
Exam #4 - Related Rates - Take 2
Mr. Leduc
Calc
Sorry about the absence. I received a call last night that mv uncle with cancer i
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I hope to be back by Monday. I will collect your test corrections from the first related
rate test and your 5 optimization questions on Monday when I am hi class.
Answer all the questions in an orderly fashion. Please clearly indicate your answer and
make sure to label your units. Each question is worth 4 points.
1) Air is being pumped into a spherical balloon at a rate of 20 in3/min. How fast is the
radius of the balloon increasing when the radius is 6 inches?
2) Oil spilled from a ruptured tanker spreads out in a circle whose are increases at a
constant rate of 6 rm'2/hr. How fast is the radius of the spill increasing when the radius is
3 miles?
Use the following information to answer questions #3-5.
A 20 foot long ladder is leaning against a wall. The bottom of the ladder is sliding away
from the wall at a rate of 2.5 ft/sec. See diagram below.
3) How fast is the top of the ladder sliding down the wall when x = 12 ft.
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4) How fast is the angle 9 changing when x = 12 feet?
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5) How fast is the area of the triangle changing when x = 12 ft?
o; A conical water tank with vertex down has a radius of 3 feet at the top and is 12 feet
high. If water flows out of the tank at a rate of 4 fWmin, how fast is the depth of the
water decreasing when the water is 6 feet deep? See the diagram below.
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7) On a dark night, a thin man 6 feet tall walks away from a lamp post 24 feet high at a
rate of 5 mph.
a) How fast is the end of his shadow moving?
b) How fast is the shadow lengthening?
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Bonus:
A right circular cylinder of constant volume is being flattened. At the moment when its
radius is 3 cm, the height is 4cm and the height is decreased at the rate of 0.2 cm/sec. At
that moment, what is the rate of change of the radius?
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