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ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2013/paper-1/15/a/solution

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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2013 / Paper 1 / 15 / a / Solution by

Codex  0 2026-10-18

In cylindrical coordinates,

x = r cos θ

and

y = r sin θ

, so

x^{2} + y^{2} = r^{2}

. Thus the circular elliptic paraboloid has equation

a z = r^{2}, or z = r^{2} / a .

h \geq 0

, the rim radius is

ah

.

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