vu (tv2894) – Homework 11 (Section 3.7) – miner – (55096)
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001
10.0 points
Find the rate at which the volume of a
sphere is changing with respect to its radius
r
when
r
= 3 cm.
1.
rate = 8
π
cm
3
/
cm
2.
rate = 32
π
cm
3
/
cm
3.
rate = 36
π
cm
3
/
cm
correct
4.
rate = 48
π
cm
3
/
cm
5.
rate = 27
π
cm
3
/
cm
Explanation:
For a sphere with radius
r
its
volume =
4
3
πr
3
.
Now the rate at which the volume is changing
with respect to
r
is the derivative of volume
with respect to
r
. Thus
rate =
d
dr
(volume) = 4
πr
2
.
Consequently, when
r
= 3 cm.,
rate = 36
π
cm
3
/
cm
.
keywords: rate of change, cube, surface area,
application
002
10.0 points
If a tank holds 2000 gallons of water, and
the water can drain from the tank in 40 min
utes, then Torricelli’s Law gives the volume
V
of water remaining in the tank after
t
minutes
as
V
= 2000
parenleftbigg
1

t
40
parenrightbigg
2
.
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 Fall '10
 Gualdini
 Calculus, Derivative, Storm, storm speed

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