What is the rate of change of the volume v of a hemisphere with respect to its radius r when r = 2?
Answer Details
To solve this problem, we need to use the formula for the volume of a hemisphere, which is V = (2/3)πr^3. We want to find the rate of change of V with respect to r, which is given by dV/dr = 2πr^2.
When r = 2, we can substitute this value into the formula to get dV/dr = 2π(2)^2 = 8π.
Therefore, the rate of change of the volume of a hemisphere with respect to its radius when r = 2 is 8π.