Answer:
150.79 ft²/s
Explanation:
area of the circle = π r²
[tex]\frac{\mathrm{d} r}{\mathrm{d} t} = 3 ft/s[/tex]
A = π r²
[tex]\frac{\mathrm{d} A}{\mathrm{d} t} = \pi r^2[/tex]
[tex]\frac{\mathrm{d} A}{\mathrm{d} t} = \pi \frac{\mathrm{d}r^2 }{\mathrm{d} t}[/tex]
[tex]\frac{\mathrm{d} A}{\mathrm{d} t} = \pi\times 2\times 8\times 3[/tex]
[tex]\frac{\mathrm{d} A}{\mathrm{d} t} = 150.79 ft^2/s[/tex]
hence the rate of total area of the disturbed water changing is equal to
150.79 ft²/s
