Question

If \[V = \frac{4}{3}\pi r^3\] ,  at what rate in cubic units is V increasing when r = 10 and \[\frac{dr}{dt} = 0 . 01\] ?  _________________

Options

•  π

• 4π
  
  

• 40π
  
  

• 4π/3

Answer 1

4π

\[\text { Given }:V = \frac{4}{3}\pi r^3 , r = 10 \text { and } \frac{dr}{dt} = 0 . 01\]
\[ \Rightarrow \frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt}\]
\[ \Rightarrow \frac{dV}{dt} = 4\pi \left( 10 \right)^2 \times 0 . 01\]
\[ \Rightarrow \frac{dV}{dt} = 4\pi\]