Length of Single Helix Turn

Calculus Level 4

\[ x = \cos \theta , \qquad y = \sin \theta, \qquad z = \theta, \qquad 0 \leq \theta \leq 2 \pi \]

Consider a single helix turn, with parameters given above.

The arc length of this single turn can be expressed as \(\sqrt{a} \pi\). Determine the value of \(a\).

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