Computing Mass When scientists make recommendations concerning environmental standards, the most important single measure is the mass of the pollutant that is present. If we have data 011 the number of particles per cubic centimeter for some particle of diameter p, then since we can compute the volume of each particle, knowing the mass density of the particle would enable us to compute the total mass of particulates. The actual density of particulate matter varies slightly with the different types of particles, but a typical density is about 1.5 g / cm3. Use this value for density in answering the questions below. 1. Write down an expression for the mass of a single particle of diameter 337 measured in am. 2. Set up an integral that represents the total mass of particles per cubic centimeter found in the atmosphere above Pasadena. Estimate the value of this integral, and explain how you made the estimation. Is your estimate an over or underestimate? 3. Write down an integral that represents the additional mass of particulate matter (per cm3) that would be removed from the air over Pasadena if the standard were changed from 10 pm to 2.5 pm. What standard would be required if we wanted to reduce tlhe mass of the particulates by 10%