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
Correct Answer: Option B
Explanation
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