(i) To find \(\theta\), first calculate the slant height of the cone using the Pythagorean theorem: \(l = \sqrt{6^2 + 8^2} = 10\) cm.

The circumference of the base of the cone is \(2\pi \times 6 = 12\pi\) cm.

The arc length of the sector is equal to the circumference of the base: \(10\theta = 12\pi\).

Solving for \(\theta\), we get \(\theta = \frac{12\pi}{10} = 1.2\pi\) or approximately 3.77 radians.

(ii) The area of the sector (paper) is given by \(\frac{1}{2} r^2 \theta\), where \(r = 10\) cm and \(\theta = 1.2\pi\).

Thus, the area is \(\frac{1}{2} \times 10^2 \times 1.2\pi = 60\pi\) cm\(^2\) or approximately 188.5 cm\(^2\).