An inverted conical water tank with a height of 12 ft and a radius of 3 ft is drained through a hole in the vertex.  If the water level drops at a rate of 1 ft/min, at what rate is the water (in cubic ft/min) draining from the tank when the water depth is 8 ft?  (hint: Use similar triangles)

Question
Asked Nov 14, 2019
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An inverted conical water tank with a height of 12 ft and a radius of 3 ft is drained through a hole in the vertex.  If the water level drops at a rate of 1 ft/min, at what rate is the water (in cubic ft/min) draining from the tank when the water depth is 8 ft?  (hint: Use similar triangles)

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Expert Answer

Step 1

Given:

An inverted conical water tank with a height of 12 ft and a radius of 3 ft.

3 ft
A
D
12 ft
E
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3 ft A D 12 ft E

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Step 2

Consider the similar triangles,

ДЕСD and AEАВ
h 12
3
h
4
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ДЕСD and AEАВ h 12 3 h 4

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Step 3

Now find the volume of the...

V = -nrh
3
2
h
h
4
1
3
h'
48
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V = -nrh 3 2 h h 4 1 3 h' 48

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Math

Calculus