Answer: dr/dt = 0.042 cm/minute
Step-by-step explanation:
Given;
dV/dt = 4cm^3/minute
t = 2.25minutes
Volume of a sphere is given as;
V = (4/3)πr^3
Change in Volume ∆V can be derived by differentiating the function.
dV/dt= 4πr^2 . dr/dt
dV/dt = 4πr^2dr/dt ....1
dV/dt is given as 4 cm^3/min
radius after 2.25 minutes can be gotten from the the volume.
Volume after 2.25mins = 4×2.25 = 9cm^3
9cm^3 = V = 4/3πr^3
r^3 = 27/4π
r = (27/4π)^1/3
From equation 1.
dr/dt = (dV/dt)/4πr^2 = 4/(4πr^2) = 1/(πr^2)
dr/dt = 1/(π(27/4π)^2/3)
dr/dt = 0.042cm/minute.
