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An inverted conical water tank with a height o 6 ft and a radius of 3 ft is drained through a hole in the vertex at a rate of 6 ft3/s. What is the rate of change of the water depth when the water depth is 5 ft​?​(Hint​: Use similar​ triangles.)

Question

An inverted conical water tank with a height o 6 ft and a radius of 3 ft is drained through a hole in the vertex at a rate of 6 ft3/s. What is the rate of change of the water depth when the water depth is 5 ft​?​(Hint​: Use similar​ triangles.)

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Step 1

Given, height of conical tank 6 ft and radius 3 ft.

3 ft
С
B
6 ft
А
in
ш
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3 ft С B 6 ft А in ш

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Step 2

In triangle ABC and triangle ADE,

АЕ АС
Similar triangle property]
DE BC
h 6
3
h
= 2
h
2
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АЕ АС Similar triangle property] DE BC h 6 3 h = 2 h 2

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Step 3

Volume of co...

V =
=-rh
..1)
3
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V = =-rh ..1) 3

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Tagged in

Math

Calculus

Derivative

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