What is the rate of change of the volume v of a hemisphere with respect to its radius r when r = 2?

Assessment: JAMB UTME - Mathematics - 2001 Subject: General Mathematics

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 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.
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