A cylindrical tank with radius 7 m is being filled with water at a rate of 2 m3/min. How fast is the height of the water increasing (in m/min)?

0.013 m/min

Explanation:

Applying,

dV/dt = (dh/dt)(dV/dh) Equation 1

Where

V = πr²h Equation 2

Where V = volume of the tank, r = radius, h = height.

dV/dh = πr² Equation 3

Substitute equation 3 into equation 1

dV/dt = πr²(dh/dt)

From the question,

Given: dV/dt = 2 m³/min, r = 7 m, π = 3.14

Substitute these values into equation 3

2 = (3.14)(7²)(dh/dt)

dh/dt = 2/(3.14×7²)

dh/dt = 0.013 m/min

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