Answer:
376.9911ft²/minute
Explanation:
In the given question the rate of chage of radius in given as
[tex]\frac{\mathrm{d}r }{\mathrm{d} t}[/tex]=5ft per minute
we know ares of circle A=pi r^{2}
differentiating w.r.t. t we get
[tex]\frac{\mathrm{d} A}{\mathrm{d} t}=2\pi r\frac{\mathrm{d}r }{\mathrm{d} t}[/tex]
Now, we have find [tex]\frac{\mathrm{d}A }{\mathrm{d} t} at r=12 feet[/tex]
[tex]\frac{\mathrm{d} A}{\mathrm{d} t}=2\times\pi\times12\times5=120\pi=376.9911ft^{2}/minute[/tex]
