A spherical balloon is inflated with gas at the rate of 20cm^3per mint. How fast the radius of the balloon changing at the instant when radius is 2cm?

Answer 1

We can use the formula for the volume of a sphere:

V = (4/3)πr^3

Taking the derivative with respect to time t,

dV/dt = 4πr^2 (dr/dt)

We are given that dV/dt = 20 cm^3/min. When r = 2 cm, we can solve for dr/dt:

20 = 4π(2^2)(dr/dt)

dr/dt = 20/(16π) = 0.397 cm/min (rounded to 3 decimal places)

Therefore, the radius is changing at a rate of approximately 0.397 cm/min when r = 2 cm.