Math Help - Cylinders

1. Cylinders

Water bubbles up at a rate of 1 cm^3/s, forimging a circular pond of depth 0.5 cm in his yard. How quickly is the surface area of the pond covering his lawn?

how would i find r to plug into the volume equation?

2. Originally Posted by Tascja
Water bubbles up at a rate of 1 cm^3/s, forimging a circular pond of depth 0.5 cm in his yard. How quickly is the surface area of the pond covering his lawn?

how would i find r to plug into the volume equation?
The volume of the pond is:

$
V=A d
$

where $d$ is the depth of the water, and $A$ is the surface area of the pond.

So the rate of change of volume is:

$
\frac{dV}{dt}=\frac{dA}{dt}\ d
$

but we are told that this is $1\ \rm{ cm^2/s}$, and as $d=0.5 \mbox{ cm}$ we have:

$\frac{dA}{dt}=1/d=2\ \rm{cm^2/s}$

RonL