Final answer:
To find the rate of change of the volume of a cone, you can use the formula V = (1/3)πr^2h. Taking the derivative with respect to time and substituting the given rates, we can find dV/dt. However, we cannot determine the rate of change of the volume with the given information.
Step-by-step explanation:
To find the rate of change of the volume of a cone, you can use the formula for the volume of a cone which is V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height. Taking the derivative of both sides with respect to time, we get dV/dt = (1/3)π(2rh)(dr/dt) + (1/3)πr^2 (dh/dt). Since the height is decreasing at a rate of 4 cm/sec (dh/dt = -4 cm/sec) and the radius is increasing at a rate of 2 cm/sec (dr/dt = 2 cm/sec), we can substitute these values into the formula to find the rate of change of the volume. So, dV/dt = (1/3)π(2r(-4)) + (1/3)πr^2(2). Simplifying the equation gives us dV/dt = -8πr + (2/3)πr^2. Since we don’t know the value of r, we can’t find dV/dt. Therefore, the rate of change of the volume cannot be determined with the given information. Hence, the correct answer is that it cannot be determined from the given information.