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Water drains from the conical tank at the rate of 5ftmin14.410Exit rate: 5 ft/mina. What is the relationship between the variables h and r in the figure above?b. How fast is the level of water dropping when h 6 ft?

Question
Water drains from the conical tank at the rate of 5ftmin
14.
4
10
Exit rate: 5 ft/min
a. What is the relationship between the variables h and r in the figure above?
b. How fast is the level of water dropping when h 6 ft?
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Water drains from the conical tank at the rate of 5ftmin 14. 4 10 Exit rate: 5 ft/min a. What is the relationship between the variables h and r in the figure above? b. How fast is the level of water dropping when h 6 ft?

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Step 1

By using the concept that the sides of similar triangles are proportional, therefore, the ratio of r and h remain same at any instant. so, we can get the relationship between r and h. 

h10
5
r 4 2
5
h =
2
2
r =h
5
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h10 5 r 4 2 5 h = 2 2 r =h 5

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Step 2

Now, we use the formula for volume of cone . By differentiating both sides with respect to t and then by substituting t...

1
V Trh=- j
3
1
4
3
75
dh
dV
dh
4
4
3h
dt 75
dt
dt
25
dh
-5=(6)
25
dt
dh
125
- ft /min
144
dt
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1 V Trh=- j 3 1 4 3 75 dh dV dh 4 4 3h dt 75 dt dt 25 dh -5=(6) 25 dt dh 125 - ft /min 144 dt

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Math

Calculus

Derivative

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