Air is being pumped into a spherical balloon so that its volume increases at a rate of 100 {cm}^3}. How fast is the surface area of the balloon increasing when its radius is 16{cm}?

Answer 1

v = 4/3 pi r^3
dv/dt = 4pi r^2 dr/dt

a = 4pi r^2
da/dt = 8pi r dr/dt
= 8pi r (dv/dt / (4pi r^2))

Now just plug in dv/dt and r