An inverted conical water tank with a height of 10 ft and a radius of 5 ft is drained through a hole in the vertex at a rate of 7 ft° / s (see figure). What is the rate of change of the water depth when the water depth is 3 ft? (Hint. Use similar triangles.)
An inverted conical water tank with a height of 10 ft and a radius of 5 ft is drained through a hole in the vertex at a rate of 7 ft° / s (see figure). What is the rate of change of the water depth when the water depth is 3 ft? (Hint. Use similar triangles.)
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An inverted conical water tank with a height of 10 ft and a radius of 5 ft is drained
through a hole in the vertex at a rate of 7 ft° /s (see figure). What is the rate of
change of the water depth when the water depth is 3 ft? (Hint. Use similar
triangles.)
Let V be the volume of water in the tank and let h be the depth of the water. Write
an equation that relates V and h.
5 A
(Type an exact answer, using n as needed.)
Differentiate both sides of the equation with respect to t.
dV
dh
%3D
10 ft
dt
dt
When the water depth is 3 ft, the rate of change of the water depth is about
(Round to the nearest hundredth as needed.)
Outflow 7 ft' /s
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