Final answer:
The student's question requires parametrizing a section of a cone using polar coordinates, with parameters r and θ. The bounds for r are from 0 to 4 due to the z-value restriction from 0 to 8 on the cone z = sqrt(8x² + 8y²).
Step-by-step explanation:
The question pertains to parametrizing a portion of the cone given by the equation z = sqrt(8x² + 8y²) and bounded by the planes z = 0 and z = 8. Parametrization is a way to represent a geometrical or algebraic entity using parameters.
To parametrize the cone, we can use polar coordinates (r, θ) in the xy-plane, where x = r cos(θ) and y = r sin(θ). Given the equation of the cone, we can write z = sqrt(8r²), which simplifies to z = 2r. Since the question restricts z to the interval [0, 8], r is thus restricted from 0 to 4.
A parametric form for the portion of the cone is therefore x = r cos(θ), y = r sin(θ), and z = 2r with 0 ≤ r ≤ 4 and 0 ≤ θ < 2π.