Let
,
, and
be the volume, radius, and depth of the water in the large pool and let
,
, and
be the volume, radius, and depth of the water in the small pool. We know that
m and
m. Since the pools are being filled at the same rate (in
),
![{\displaystyle {\frac {dV_{1}}{dt}}={\frac {dV_{2}}{dt}}.}](https://wiki.ubc.ca/api/rest_v1/media/math/render/svg/573ef226315168f6bdf46c1adfab248d951f2e77)
We know that
and we want to find
.
By the volume formula for a cylinder,
and
.
Note that
and
are constants. The variables of the problem are
and
Since
,
.
Hence, the water depth in the the larger pool is increasing at a rate of
.