Page 69 - How To Solve Word Problems In Calculus

Step2
Let V represent the volume of water in the tank.

dV
Given: =−2000 ← dV /dt is negative since the vol-
dt ume of water in the trough is get-
ting smaller.

dh
Find: when h = 20
dt
h
The area of a trapezoid is (a + b)
2
Step3
h
The cross-sectional area of the water is A = (x + 30). The
2
volume of water V = l × A. l is the length of the trough so
h
V = l · (x + 30). Since the units in the problem must be con-
2
sistent, we take l = 200 cm. Thus V = 100h(x + 30). Since x is
not mentioned in either the “Given” or the “Find” in step 2,
we should eliminate x from this equation. To accomplish this,
we observe similar triangles.

15 30 D 15 E

50
y 30 B y
C
h
30 A
x

In this figure
ABC is similar to
ADE. Since their corre-
sponding sides are proportional,

y h
=
15 50
3
y = h
10

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