Careful! Duck!

Calculus Level 3

Min, the perfectly spherical duck, is happily picking up cubical seeds to eat. He grows in volume at a rate of 9 cubic feet per day. When Min's radius is 7 feet, at what rate (in square feet per day) is his surface area growing at that instant?

\frac {18}{7}

\frac {9}{14}

\frac {12}{13}

\frac {17}{6}

1 solution

Vishnu C
Apr 27, 2015

$V=4/3\pi r^{ 3 }.\\ dV/dt=9=4\pi r^{ 2 }dr/dt.\\ dr/dt=9/4\pi r^{ 2 }\\ S=4\pi r^{ 2 }\\ dS/dt=8\pi rdr/dt\\ \Rightarrow dS/dt=18/r=18/7\quad square\quad feet\quad per\quad day.$

I am so amused by a "perfectly spherical duck eating cubical seeds".

Calvin Lin Staff - 6 years, 1 month ago

Exactly sameway... :)

Nithin Nithu - 5 years, 6 months ago

Careful! Duck!

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