 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ia/paper-3/11a/i/solution

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

The ball volume is

V_{n} (R) = \frac{π ^{n /2} R ^{n}}{Γ ( n /2 + 1 )} .

For

n = 2 m

this is

π^{m} R^{2 m} / m!

; for

n = 2 m + 1

it is

2^{2 m + 1} m! π^{m} R^{2 m + 1} / (2 m + 1)!

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