The diagram shows a sector of a circle of radius \(r\text{ cm}\), centre \(O\), with \(\angle AOB=\frac{2\pi}3\) radians. The shaded region lies between chord \(AB\) and arc \(AB\).

(a) Show its area \(A\text{ cm}^2\) is approximately \(0.614r^2\). [2]

The radius increases at a constant rate of \(0.4\text{ cm s}^{-1}\).

(b)(i) Find the rate of increase of the shaded area when \(r=20\). Give your answer to 2 significant figures. [3]

(b)(ii) Find the rate of increase of the length of arc \(AB\). Give your answer to 2 significant figures. [3]