SUMMARY
The problem involves calculating the total surface area of N spherical droplets formed from 30.0 cm³ of gasoline, with each droplet having a radius of 2.00 x 10^-3 m. The surface area (SA) of a single droplet is calculated using the formula SA = 4 * π * r², resulting in an individual surface area of 5.03 x 10^-9 m². The total volume of the droplets can be determined using the volume formula V = 4/3 * π * r³, leading to the conclusion that the total volume before atomization equals the total volume after. By equating the known volume of gasoline to the volume of the droplets, the number of droplets (N) can be derived, allowing for the calculation of the total surface area.
PREREQUISITES
- Understanding of geometric formulas for surface area and volume of spheres
- Familiarity with unit conversions (cm³ to m³)
- Basic algebra for solving equations
- Knowledge of constants such as π (pi)
NEXT STEPS
- Calculate the total volume of N spherical droplets using the formula V = N * (4/3 * π * r³)
- Explore the implications of surface area in fluid dynamics and atomization processes
- Investigate the effects of droplet size on combustion efficiency in gasoline engines
- Learn about the applications of spherical droplet calculations in chemical engineering
USEFUL FOR
Students in physics or engineering, particularly those studying fluid mechanics, as well as professionals involved in combustion research and atomization technology.