What is the rate of change of the volume v of a hemisphere with respect to its radius r when r = 2?
Question 1 Report
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 find the rate of change of the volume of a hemisphere with respect to its radius, we need to differentiate the formula for the volume of a hemisphere with respect to its radius. The formula for the volume of a hemisphere is V = (2/3)πr^3. Taking the derivative of this formula with respect to r gives us dV/dr = 2πr^2. Therefore, the rate of change of the volume of the hemisphere with respect to its radius is 2πr^2. When r = 2, the rate of change is 2π(2^2) = 2π(4) = 8π. Thus, the answer is 8π.
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