SUMMARY
The volume of the space bounded by the surface defined by z = x^2 + y^2 = 9 and the xy-plane is confirmed to be 9, contrary to the answer key which states 18. Multiple participants in the discussion, including the original poster and their group mate, reached the same conclusion of 9 after performing the calculations. This discrepancy highlights the need for careful verification of answer keys in educational settings.
PREREQUISITES
- Understanding of triple integrals in calculus
- Familiarity with cylindrical coordinates
- Knowledge of volume calculation for bounded regions
- Basic proficiency in mathematical reasoning and problem-solving
NEXT STEPS
- Review the process of calculating volumes using triple integrals
- Study the conversion between Cartesian and cylindrical coordinates
- Practice problems involving bounded volumes in calculus
- Examine common errors in answer keys and how to verify solutions
USEFUL FOR
Students preparing for calculus exams, educators verifying answer keys, and anyone interested in mastering volume calculations in multivariable calculus.