Question

a spherical balloon is inflated at a rate of 36pi cm³/sec. How fast is the radius of the balloon increasing when radius is 7cm?

Answer 1

$V=\frac{4}{3}\pi r^3.$

$\frac{dV}{dt}=4\pi r^2\frac{dr}{dt}.$

$\frac{dr}{dt}=\frac{\frac{dV}{dt}}{4\pi r^2}$

When $r=7:$ $\frac{dr}{dt}=\frac{36}{4\pi *7^2}=\frac{9}{49\pi}\approx0.0585\;\frac{cm}{sec}.$