Gauge Diameter

Source: Dec 2025, Task 1 (DTU 02002/02003). Study solution — not an official answer key.

Problem

An n-gauge ball has volume V/n with V = 40 cm³, so (π/6) d³ = V/n, i.e. d = (6V / (n π))^1/3.

Write gauge_diameter(n) returning the diameter in cm.

Example

>>> gauge_diameter(12)
1.8533610896304256

Use math.pi and raise to the power 1/3 (or **(1/3)).

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Solution

import math

def gauge_diameter(n):
    V = 40
    return (6 * V / (n * math.pi)) ** (1 / 3)