Find the rate of change of the volume, V of a sphere with respect to its radius, r when r = 1.
A
12π
B
4π
C
24π
D
8π
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
Volume of sphere, V = 4/3 x πr3
Rate of change of V = dv/dr
Thus if V = 4/3 x πr3,
=> dv/dr = 4πr2
At r = 1, Rate = 4 x π x 1 = 4π
Source: Myschool Past Questions Archive (Record #2559)