Page 70 - How To Solve Word Problems In Calculus

3
Since x = 2y + 30 (see diagram), it follows that x = h + 30
5
and

V = 100h(x + 30)

3
= 100h h + 60
5
2
V = 60h + 6000h

Step4

dV dh
= (120h + 6000)
dt dt

Step5
dV
We substitute =−2000 and h = 20 into the result of
dt
step 4.

dh
−2000 = 8400
dt
dh 2000 5
=− =− cm/min
dt 8400 21

The minus sign indicates that the water level is falling at the
5
rate of cm/min.
21

EXAMPLE 10

Water is being pumped into a conical tank at the rate of
3
100 ft /min. The height of the tank is 20 ft and its radius is
5 ft. How fast is the water level rising when the water height is
10 ft?

57