Page 72 - How To Solve Word Problems In Calculus

Replacing r in the volume formula, we get V as a function of h:

2
π h
V = h
3 4
π
V = h 3
48
Step4
dV 3π dh
= h 2
dt 48 dt
π 2 dh
= h
16 dt
Step5
π 2 dh
100 = (10)
16 dt
100π dh
100 = ·
16 dt
dh
1600 = 100π
dt

dh 16
=
dt π
16
The water level is rising at the rate of ft/min.
π
Supplementary Problems

1. A spherical snowball is melting in such a way that its surface area
2
decreases at the rate of 1 in /min.
(a) How fast is its radius shrinking when it is 3 in?
(b) How fast is its volume shrinking when its radius is 3 in?
2. Two cars begin a trip from the same point P.Ifcar A travels north at
the rate of 30 mi/h and car B travels west at the rate of 40 mi/h,
how fast is the distance between them changing 2 hours later?
3. Ship A is 70 km west of ship B and is sailing south at the rate of
25 km/h. Ship B is sailing north at the rate of 45 km/h. How fast is
the distance between the two ships changing 2 hours later?
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