Answer:
[tex]\frac{dr}{dt}=0.11062ft/sec[/tex]
Step-by-step explanation:
From the question we are told that:
Radius [tex]r=5ft[/tex]
Height [tex]H=15ft[/tex]
Rate [tex]R=15ft/3sec =5ft/s[/tex]
Surface Radius [tex]R_{surf}=2.2ft[/tex]
Generally the equation for Volume is mathematically given by
[tex]V=\frac{1}{3}\pi*r^2h[/tex]
Since radius to height ratio gives
[tex]\frac{r}{h}=\frac{5}{15}[/tex]
[tex]\frac{r}{h}=\frac{1}{3}[/tex]
[tex]h=3r[/tex]
Therefore
[tex]V=\frac{1}{3}\pi*r^2(3r)[/tex]
[tex]V=\pi r^3[/tex]
Generally the equation for Change of Volume is mathematically given by
[tex]\frac{dv}{dt}=\pi \frac{d}{dt}(r^3)[/tex]
[tex]\frac{dv}{dt}=\pi 3*r^2 \frac{dr}{dt}[/tex]
[tex]\frac{dv}{dt}=\pi 3*(2.2)^2 \frac{dr}{dt}[/tex]
[tex]\frac{dr}{dt}=\frac{5}{45.62}[/tex]
[tex]\frac{dr}{dt}=0.11062ft/sec[/tex]
