The discussion centers on calculating the volume of the solid beneath the plane defined by the equation z = 4x and above the circular region described by x² + y² = 16 in the xy-plane. Participants clarified that part of the plane z = 4x does indeed lie above the xy-plane, indicating that a solid exists between the two surfaces. The correct approach involves using double integrals and polar coordinates to evaluate the volume, rather than concluding that the volume is zero.
PREREQUISITESStudents studying calculus, particularly those focusing on multivariable calculus and volume calculations, as well as educators looking for examples of integrating over circular regions.
Part of the z = 4x plane lies above the xy plane. Did you draw a sketch of the plane and the circle?nate9519 said:Homework Statement
find the volume of the solid below the plane z = 4x and above the circle x^2 + y^2 = 16 in the xy plane
Homework Equations
The Attempt at a Solution
This totally confused me. I didn't think the plane z = 4x sat above the xy plane.
nate9519 said:If that is true then there would be no solid between the two graphs. I ended up putting zero for the answer. was I right or wrong