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

Answer 1

We can use the formula for the volume of a sphere: V = (4/3)πr^3, where V is the volume and r is the radius.

Differentiating both sides with respect to time (t), we get:

dV/dt = 4πr^2 (dr/dt)

where dV/dt is the rate of change of volume (which is 20 cm^3/min), and dr/dt is the rate of change of radius (which we need to find).

At the given radius of 2 cm, we can plug in the values and solve for dr/dt:

20 = 4π(2)^2 (dr/dt)
dr/dt = 20 / (16π)
dr/dt ≈ 0.397 cm/min

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