What is the rate of change of the volume V of a hemisphere with respect to its radius r when r = 2?
Answer Details
The formula for the volume of a hemisphere is given by (2/3)πr^3, where r is the radius. To find the rate of change of the volume with respect to the radius, we need to take the derivative of this formula with respect to r.
So, dV/dr = (2/3) * π * 3r^2 * dr/dr = (2/3) * π * 3r^2 = 2πr^2.
Now, when r = 2, the rate of change of the volume with respect to the radius is given by 2π * 2^2 = 8π.
So, the answer is 8π.