A circular balloon is inflated with air flowing at a rate of 10cm3/s. How fast is the radius of the

A circular balloon is inflated with air flowing at a rate of 10cm3/s. How fast is the radius of the ballon increasing when the radius is 2cm?

The volume (V) of the balloon with radius (r) is:
V = 4/3πr^3

Differentiating with respect to t, we get:
dV/dt = 4/3π * 3r^2 * dr/dt
dV/dt = 4πr^2 * dr/dt

The rate of change of the volume is:
dV/dt = 10cm^3s^−1

So, we find dr/dt:
dr/dt = 1/4πr^2 * dV/dt
dr/dt = 10/4πr^2
dr/dt = 5/2πr^2

Therefore, dr/dt(2cm) is:
dr/dt(2cm) = 5/2π(2)^2
dr/dt(2cm) = 5/2π4
dr/dt(2cm) = 5π/8