WS 22 – Related Rates
Name _______________________________ # ____
(4 pages)
1.
A pebble is dropped in still water, forming a circular ripple whose radius is expanding at a
constant rate of 10 cm/sec.
Find a formula giving the area enclosed by the ripple as a function of
time.
When the radius is 20 cm, how fast is the area enclosed by the ripple increasing?
10 cm/sec =
gG
g±
²³´µ = ¶´
·
²³¸µ = ¶¹´³¸µº
·
g»
g±

G¼·½
=?
g»
gG
= 2¶´
g»
g±
= 2¶¹´³¸µº ∗
gG
g±
´ → 20
² →
g»
g±
¾
G¼·½
= 2¶¹´³¸µº ∗
gG
g±
g»
g±
¾
G¼·½
= 2¶¹20º ∗ 10 = 400¶ ¿À
·
/ÁÂ¿
The area is increasing at a rate of 1,256.64 square centimeters per second when the radius is
20 centimeters.
2.
(A) When the radius of a balloon (assume it is a sphere) is 10 cm, at what rate is the volume of the
balloon changing with respect to its radius?
Ã →
gÄ
gG
=?
Ã³´µ =
Å
Æ
¶´
Æ
´ → 10
gÄ
gG
= 4¶´
·
gÄ
gG
¾
G¼Ç½
= 4¶³10µ
·
= 400¶ ¿À
·
(B) If the radius of the spherical balloon is increasing by 0.5 cm/sec, how fast is the air being blown
into the balloon when the radius is 6 cm?
Ã →
gÄ
g±
=?
Ã³¸µ =
Å
Æ
¶¹´³¸µº
Æ
´ → 6
gG
g±
= 0.5
gÄ
g±
= 4¶´
·
∗
gG
g±
gÄ
g±
¾
G¼È
= 4¶³6µ
·
∗ É
Ç
·
Ê = 72¶ ¿À
Æ
/ÁÂ¿
The volume is increasing at a rate of about 226.2 cubic centimeters per second when the
radius is 6 centimeters
.
3.
The mass of a circular oil slick of radius
r
is
(
ln(1
))
M
K r
r
=

+
, where
K
is a positive constant.
What is the relationship between the rate of change of the radius with respect to time and the rate of
change of the mass with respect to time?
(
ln(1
))
M
K r
r
=

+
gË
g±
= Ì ÉÍ −
Í
ÍÎÏ
Ê ∗
gG
g±
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document4.
(Text 4.6 #16)
The volume of a square base pyramid is
g =
G
±
²
³
ℎ
.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '13
 Wood
 Orders of magnitude

Click to edit the document details