# If a cylindrical tank with radius 5 meters is being filled with water at a rate of 3 cubic meters per minute, how fast is the height of the water increasing?

In general

- find a formula to relate the 2 variables
- substitute values to remove the constant variables
- implicitly differentiate wrt time (most often the case)
- substitute the given rate
- and solve for the desired rate.

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To find how fast the height of the water in the cylindrical tank is increasing, you can use related rates.

Given:

- Radius of the cylindrical tank, ( r = 5 ) meters
- Rate of water being filled, ( \frac{dV}{dt} = 3 ) cubic meters per minute

You can use the formula for the volume of a cylinder: ( V = \pi r^2 h ), where ( V ) is the volume, ( r ) is the radius, and ( h ) is the height.

Differentiate the volume formula with respect to time ( t ) to find ( \frac{dh}{dt} ), the rate at which the height of the water is increasing.

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