(i) To find the length of OB, use the cosine rule in the right-angled triangle OAB:

\(OB = \frac{OA}{\cos(\angle AOB)} = \frac{6}{\cos(0.6)} = 7.270 \text{ cm}\)

(ii) To find the perimeter of the metal plate, calculate the lengths of AB and the arc BC:

\(AB = OA \times \tan(\angle AOB) = 6 \times \tan(0.6) = 4.1 \text{ cm}\)

The arc length BC is given by:

\(s = r \theta = 7.27 \times (\frac{\pi}{2} - 0.6) = 7.06 \text{ cm}\)

Thus, the perimeter is:

\(6 + 7.27 + 7.06 + 4.1 = 24.4 \text{ cm}\)

(iii) To find the area of the metal plate, calculate the areas of triangle OAB and sector OBC:

The area of triangle OAB is:

\(\frac{1}{2} \times 6 \times 7.27 \times \sin(0.6) = 12.31 \text{ cm}^2\)

The area of sector OBC is:

\(\frac{1}{2} \times 7.27^2 \times (\frac{\pi}{2} - 0.6) = 25.65 \text{ cm}^2\)

Thus, the total area is:

\(12.31 + 25.65 = 38.0 \text{ cm}^2\)