The Swimming Pool
The cross sections of two swimming pools that are being
filled at a constant rate are shown below.
For pool B, the two sections to
consider are the bottom of the deep end of the pool up to where the shallow
end starts and the rest of the pool. Both of these
portions are rectangular prisms. The water depth will
increase at a certain constant rate until the water level reaches the deep
end edge of the shallow end of
the pool. Then, as the water begins to fill the shallow end, the water
depth increases at a slower but still constant rate until the pool is full.
This is because the deep
end of the pool is a prism with a smaller base than the base of the prism
that is the whole pool.
1. For each pool, write a description of how the depth in
meters, d, of the water in the pool varies with time in minutes, t, from
the moment the empty pool begins to fill.
For pool A, the cross section of
the pool is a rectangle. If water is flowing into the pool at a constant
rate, the geight of the pool wil rise at a constant rate.
2. Sketch a graph to show how the depth of the water
in each pool varies with time from the moment the empty pool begins to fill.
Blue - Pool B
Red - Pool A
Green - Pool B is standing in the shallow end