Final answer:
By applying related rates in calculus, the rate at which the water level is rising in the inverted cone is calculated to be 0.95 cm/min, which corresponds to option (a).
Step-by-step explanation:
The question involves using the concept of related rates, which falls under calculus in mathematics. Specifically, we are asked to find out how fast the water level is rising in an inverted cone when water is flowing into it at a rate of 2 cm³/min. Given that the cone's height is 16 cm and the radius is 4 cm, we can use the formula for the volume of a cone (V = 1/3 * π * r^2 * h) to relate the volume and dimensions of the cone.
To find how fast the water level is rising, we need to apply the related rates technique. We know that DV/dt = 2 cm³/min and we seek dh/dt when h = 16 cm and r = 4 cm. Because the problem states that the cone is 'inverted', and water is flowing into it, h will decrease as V increases. Since r and h are related by the similarity of triangles (r/h = 4/16), we can express r in terms of h and then differentiate the volume concerning time. When we differentiate the volume formula and substitute the values, we will find dh/dt, which represents how fast the water level is rising.