An island is in the approximate shape of a prism with a trapezium-shaped cross-section. (The cross-section is shown in a diagram. Each square on the grid represents an area 100m by 100m.) If the island is 1.2km long, find the approximate volume of above-sea-level land.
The area of the island is 0.18km².
First, let's find the width of the island by dividing the total area by the length:
0.18 km² / 1.2 km = 0.15 km
Now, let's find the area of the trapezium-shaped cross-section using the formula for the area of a trapezium:
Area = 1/2 (a + b)h
Where a and b are the length of the parallel sides of the trapezium and h is the distance between them.
We can see from the diagram that the base of the trapezium is 0.15 km and the height is 0.12 km (since each square on the grid represents 100m, and there are 1.2 km in total).
Plugging these values into the formula:
Area = 1/2 (0.15 km + 0.12 km) * 0.12 km
Area = 1/2 (0.27 km) * 0.12 km
Area = 0.027 km²
Now, to find the volume of above-sea-level land, we multiply the area by the length of the island:
Volume = 0.027 km² * 1.2 km
Volume = 0.0324 km³
Therefore, the approximate volume of above-sea-level land on the island is 0.0324 km³.