2026 CCHMS P2 Q9

A coastal city has an existing sea dike to protect its low-lying land from rising sea levels. The dike has a uniform trapezoidal cross-section, \(ABCD\), as shown in Diagram (a). Its crest, \(BC\), is 8 m wide and its base, \(AD\), is 38 m wide. The crest is 6 m above the current mean sea level. The seaward face rises over a horizontal distance of 18 m from \(A\) to \(F\).

1. Find the angle, \(\theta\), that the seaward face of the dike makes with the horizontal.[1]

The dike extends 10 km along the coast and has the same cross-section throughout its length.

2. Find the volume of fill used to build the 10 km dike. Leave your answer in cubic metres.[2]

The graph below shows the projected rise in mean sea level (above the current mean sea level) under two global emission scenarios, up to the year 2150.

For safety, engineers require the dike crest to remain at least 4.5 m above the projected mean sea level. The width of the crest and gradients of the sloping faces remain unchanged as shown in Diagram (b).

You are an engineer preparing a budget proposal for the city council to protect the coast. The budget must include:

• the cost of additional fill required to raise the existing dike so that it meets the safety requirement in the year 2150 under the high-emissions scenario; and
• the cost of maintaining the dike by replacing fill lost through erosion over the following 50 years.

3. Using the graph and the cost information provided, recommend a budget for the council to approve. Justify your recommended budget with clear workings.[8]