Isso ta me cheirando a taxas relacionadas!
H=10m
R=4m
a)
R/H = 4/10= 2/5
R= 2H/5
b)
[tex]v = \frac{1}{3} \pi {R}^{2} H \\ v = \frac{1}{3}\pi { (\frac{2}{5}H)}^{2} H \\ v = \frac{1}{3}\pi \frac{4}{25}{H}^{2} .H[/tex]
[tex]v = \frac{1}{3}\pi. \frac{4}{25} {H}^{3} [/tex]
[tex] \frac{dv}{dt} = \frac{1}{3}.\pi \frac{4}{25}3.{H}^{2}. \frac{dH }{dt} \\ \frac{dv}{dt} = \frac{4}{25}\pi {H}^{2} .\frac{dH }{dt} [/tex]
dv/dt= 5m³/h
H=6m
dH/dt=?
[tex]5 = \frac{4}{25}\pi. {6}^{2} . \frac{ dH}{dt} \\ \frac{dH}{dt} = \frac{25.5}{144\pi} = \frac{125}{144\pi} m/h[/tex]
