Answer:
E 1 cm/min 98π
Step-by-step explanation:
We know the volume of a sphere V = 4πr³/3. Now the rate of change of volume with respect to time dV/dt = dV/dr × dr/dt where dV/dr is the rate of change of volume with respect to the radius and dr/dt is the rate of change of radius with respect to time.
Now, dV/dt = -2 cm³/min since it is decreasing
dV/dr = 4πr²
So, dV/dt = dV/dr × dr/dt
-2 cm³/min = 4πr²dr/dt
dr/dt = -2 cm³/min ÷ 4πr²
when r = 7 cm,
dr/dt = -2 cm³/min ÷ 4π(7 cm)²
dr/dt = -1 cm³/min (2π × 49 cm²)
dr/dt = -1 cm/min 98π
So, the radius is changing (decreasing) at a rate of 1 cm/min 98π
