(i) To find angle AOB, use the sine rule in the right triangle formed by the radius and half of AB. The sine of half the angle is given by:

\(\sin(\frac{1}{2} \text{angle}) = \frac{16}{20}\)

Solving for the angle, we find:

\(\text{Required angle} = 1.855 \text{ radians}\)

(ii) The area of sector AXBO is calculated using the formula:

\(\frac{1}{2} r^2 \theta\)

Substituting the values, we get:

\(\frac{1}{2} \times 20^2 \times 1.855 = 371 \text{ cm}^2\)

(iii) The area of the new cross-section is found by subtracting the area of the rectangle and the sector from the area of the circle, and then adding the area of the triangle:

\(\pi r^2 - l \times b - \frac{1}{2} r^2 \theta + \frac{1}{2} bh\)

Substituting the values, we get:

\(\pi \times 20^2 - 32 \times 18 - \frac{1}{2} \times 20^2 \times 1.855 + \frac{1}{2} \times 32 \times 18 = 502 \text{ cm}^2\) (accept 501)