MATHEMATICS
JAMB 2004 - Question 38
Mathematics 2004 JAMB Past Questions - Question 38: What is the rate of change of the volume of a hemisphere with respect to its radius r when r=2?
A:
B:
C:
D:
Correct Answer
D
Explanation
The volume (V) of a hemisphere is given by the formula:V = (2/3)πr³To find the rate of change of the volume with respect to the radius (dr/dV), we need to differentiate the volume formula with respect to r.dV/dr = d/dx [(2/3)πr³]Using the power rule of differentiation, we can differentiate each term:dV/dr = (2/3)π * 3r²Simplifying further:dV/dr = 2πr²Now, we can find the rate of change of the volume with respect to the radius (dr/dV) when r = 2:dr/dV = 2π(2)²dr/dV = 2π(4)dr/dV = 8πTherefore, when r = 2, the rate of change of the volume of the hemisphere with respect to its radius is 8π.
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