Digging in his backyard, Dennis accidentally breaks a pipe a

[kimmy_koo51]

Digging in his backyard, Dennis accidentally breaks a pipe attached to his water-sprinkler system. Water bubbles up at rate of 1cm3/s, forming a circular pond depth o.5 cm in his yard. How quickly is the surface area of the pond covering his lawn?

 

[skeeter]

you are given dV/dt = 1 cm³/s

volume of the "pond" is \(\displaystyle \L V = \pi r^2 h\) ... h will be a constant 0.5 cm

using this equation, take the derivative w/r to time, then solve for \(\displaystyle \L 2\pi r \frac{dr}{dt}\).

surface area of the pond is \(\displaystyle \L A = \pi r^2\)

... find dA/dt.