February 22, 2021

Solve Monday's Problem

Environmental engineers work with other engineers, scientists and experts to control water and air pollution, as well as its impact on public health, waste disposal, recycling and more. Environmental engineers at the Environmental Protection Agency (EPA) work to clean up some of the country’s most contaminated toxic waste sites, called Superfund sites. At certain Superfund sites, where toxic waste has caused serious environmental issues, groundwater—water that is found underground in the gaps between layers of rock, soil or sand—is contaminated, which can lead to chemicals in recreational lakes, drinking water and wildlife habitats.

1.1) The amount of contaminant in groundwater is reported using a measurement called parts per billion (ppb). This is calculated as:

For groundwater to be considered safe, the amount of contaminant in the groundwater must be at or below 5 ppb. What is the maximum number of micrograms of contaminant that could be in 7 × 108 micrograms of safe groundwater?

1.2) A drum of dry-cleaning solvent, a toxic chemical, is dumped and seeps into the soil, contaminating the groundwater below. This space where contaminants have spread is called a plume. Exactly one year after the solvent was dumped, the plume forms a square pyramid underground that has spread to a depth of 50 m and 30 m across at its base edge. What is the volume of the plume after one year?

1.3) Each year after the first year, the depth of the plume in problem 1.2 triples and the base edge of the plume doubles. What is the volume of the plume exactly 4 years after the solvent was dumped?

1.4) When environmental engineers arrive to clean up the contaminated site referenced in problems 1.2 and 1.3, they must block off all the space above ground over any part of the plume to ensure the cleanup process is not disturbed. If the engineers begin cleanup exactly 4 years after the solvent was dumped, how many square meters must they block off above ground to cover the entire plume (in thick purple outlines below)?