 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ia/paper-3/11b/a/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

x = a u, y = b v, z = c w .

The ellipsoid becomes the unit ball and the Jacobian determinant is

ab c

. Therefore

Vol = ab c Vol (B_{1}) = \frac{4 πab c}{3},

assuming

a, b, c > 0

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