(a(i))[2]
Determine the length and width of rectangle $R$.
(a(ii))[2]
Rectangle $S$ is mathematically similar to rectangle $R$. The perimeter of rectangle $S$ is $30.6\text{ cm}$. Calculate the length of rectangle $S$.
(b(i))[2]
A piece of card is a sector of a circle with sector angle $75^\f$ and radius $8\text{ cm}$. Find an expression, in terms of $\pi$, for the arc length of the sector.
(b(ii))[5]
The card makes the curved surface area of a cone. The cone is completely filled with water. Calculate the volume of water in the cone. (Volume of a cone $= \frac{1}{3}\pi r^2 h$.)