A cylindrical tank with radius 7 m is being filled with water at a rate of 4 m3/min. How fast is the height of the water increasing? m/min

The volume V of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height.

Given that the radius r is 7 m and the volume V is increasing at a rate of 4 m³/min, we want to find dh/dt, the rate at which the height h is increasing.

We can start by differentiating both sides of the volume formula with respect to time t to get dV/dt = πr²dh/dt.

We can then solve for dh/dt to get dh/dt = dV/dt / (πr²).

Substituting the given values into this equation gives us dh/dt = 4 m³/min / (π*(7 m)²) = 4 m³/min / (153.9380400259 m²) = 0.02598 m/min.

So, the height of the water is increasing at a rate of approximately 0.026 m/min.