Answer:
dr/dt = -2 cm/s.
Explanation:
The volume of a cone is given by:
[tex]V=\frac{1}{3} \pi r^{2}h[/tex] (1)
Let's take the derivative with respect to time in each side of (1).
[tex]\frac{dV}{dt}=\frac{1}{3} \pi \frac{d}{dt}(r^{2}h)=\frac{1}{3} \pi \left(2r\frac{dr}{dt}h+r^{2}\frac{dh}{dt} \right)[/tex] (2)
We know that:
We can calculate how fast is the radius changing using the above information.
[tex]0=\frac{1}{3} \pi \left( 2\cdot 4\cdot \frac{dr}{dt} \cdot 10 + 4^{2}\cdot 10)\right[/tex]
Therefore dr/dt will be:
[tex]\frac{dr}{dt}=-\frac{160}{80}=-2 cm/s[/tex]
The minus signs means that r is decreasing.
I hope it helps you!
