Question: a. Show that when you express ds 2 = dx 2 + dy 2 + dz 2 in terms of cylindrical coordinates, you get ds

a. Show that when you express ds2 = dx2 + dy2 + dz2 in terms of cylindrical coordinates, you get ds2 = dr2 + r2 dθ2 + dz2.

b. Interpret this result geometrically in terms of the edges and a diagonal of a box. Sketch the box.

c. Use the result in part (a) to find the length of the curve r = eθ, z = eθ, 0 ≤ θ ≤ ln 8.

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