Final answer:
The calculated density of the pheromone is 0.00632 g/L, which is not listed among the provided options. To calculate this, we first converted the radius and height into meters, calculated the volume in cubic meters, converted it to liters, and then divided the mass by the volume to find the density.
Step-by-step explanation:
To calculate the density of the pheromone in g/L, we need to find the volume of the airspace first and then use the mass of the pheromone to find its density. The volume V of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height. In this case, the radius r is 0.4 miles and the height h is 40 feet. However, we need to convert these measurements into consistent units. Since we want the density in g/L, we need the volume in liters (L).
First, convert the radius in miles to meters: r = 0.4 miles × 1,609.34 meters/mile = 643.736 meters.Convert the height in feet to meters: h = 40 feet × 0.3048 meters/foot = 12.192 meters.Now calculate the volume in cubic meters: V = π × (643.736)^2 × 12.192 = 15,816,543.05 m^3.Convert cubic meters to liters: 1 m^3 = 1,000 L, so V = 15,816,543.05 m^3 × 1,000 L/m^3 = 15,816,543,050 L.Now we can calculate the density using the mass of the pheromone: density = mass / volume = 1 x 10^8 g / 15,816,543,050 L = 0.00632 g/L.
This density value is not explicitly listed in the options provided (a) 1.03 g/L, (b) 3.12 g/L, (c) 5.43 g/L, or (d) 7.65 g/L, indicating that there may have been an error in the question or in the calculation. If we check the units and calculation steps carefully, it's clear that we must re-evaluate the given options, as none of them match the calculated value.