Question

The radius of an air bubble is increasing at the rate of $2cm/s$. At what rate is the volume of the bubble increasing when the radius is $2cm$?

• A. $12\pi c{m}^3/s$
• B. $8\pi c{m}^3/s$
• C. $32\pi c{m}^3/s$
• D. $16\pi c{m}^3/s$

Answer 1

The correct option is C $32\pi c{m}^3/s$

Volume of the air bubble
$V=\frac{4}{3}\pi r^3\Rightarrow \frac{dV}{dt}=4\pi r^2\frac{dr}{dt}\Rightarrow \frac{dV}{dt}=4\pi \times 2^2\times 2=32\pi c{m}^3/s$