Answer:
0.013 cm/minute
Explanation:
We are given;
Volume rate; dV/dt = 800 cm³/min
Now, volume of a sphere is given by the formula;
V = (4/3)πr³
We want to find the rate at which the radius of the balloon is changing. This is represented by dr/dt.
Now, dr/dt will be gotten from the relation;
dr/dt = dV/dt ÷ dV/dr
Now, dV/dr = 3 × (4/3)πr²
dV/dr = 4πr²
Thus;
dr/dt = 800/(4πr²)
At r = 70 cm
dr/dt = 800/(4π × 70²)
dr/dt = 0.013 cm/minute
