Answer:
1/50π cm/min
Step-by-step explanation:
The rate of change of the sphere is 2cm/min
dv/dt = 2cm/min
The volume of a sphere is given by
V= 4/3 πr^3
Since the diamter is 10cm, then the radius is 5cm
Therefore
Dv/dt = dr/dv * dv/dt
To find Dr/dv we differentiate
V= 4/3 πr^3 which will give 4πr^2
2 = 4πr^2* dv/Dr
2/4πr^2 = dv/dt
Dv/dt = 2/ 4×5×5π
Dv/dt= 1/50π
The volume is increasing at the rate of 1/50π
