 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2016/paper-2/12/a/solution

Put

R = ∣ b ∣

so that the radial range respects the stated allowance

b \neq = 0

. With the azimuth measured from the starting meridian, the cylindrical coordinates of the curved surface satisfy

0 \leq r \leq R, 0 \leq θ \leq α, z = a (1 - \frac{r ^{2}}{b ^{2}}) .

r = 0

all azimuths describe the same apex. The surface is a sector of an elliptic paraboloid.

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