Rainfall is measured in units of length. It is quoted in millimetres falling on any flat, unobstructed area within the region receiving the rainfall. The amount of rainfall is recorded by a rain gauge as the height in millimetres. The Bureau of Meteorology publishes the amount of rainfall in all major population centres as an accrual over 24 hours from 9:00 to 9:00 each morning. Searching the website may lead you to a table showing the amount of rainfall every 10 minutes. A rain gauge at home can be fun for children, measuring and recording the data. Below is a hyperlink to a fact-sheet on choosing the appropriate water storage capacity for your home. Even if renting, you can perhaps arrange to install a small to medium sized water tank that could supplement your use of town water. Read the fact sheet on choosing the right sized water tank; then answer the following questions. http://www.nedlands.wa.gov.au/sites/default/files/Rainwater%20tank%20factsheet.pdf

(a) The fact-sheet claims that 1 of rain, falling on an area of 1 m2 , will deliver 1 L of rainwater into your water tank. Use your mathematical skill to show that this claim, as presented in the fact-sheet, is correct. Helpful information: 1 L is 1000 cm3 . This calculation will work best using centimetres.

(b) A modern, medium-sized home may have a rooftop water collection area of 200 2 , and should get by with a rainwater tank of between 2000 and 10 000 L. Suppose that, to go with the 200 2 roof of your house, you would like a rainwater storage capacity of 5000 L. Calculate the rooftop rainfall (in mm, as shown by a rain gauge) that would fill a 5000 L water tank. [Note that 1 m3 is 1000 L.]

(c) You select a narrow tank that fits beside the wall of your house. The top (or plan view) of the water tank is a flat, composite shape with two semi-circular ends and a long straight section in-between. Thus the tank is 300 mm wide, and altogether 3500 mm long, as shown:

(i) Calculate the perimeter of the top of the tank (in millimetres and correct to the nearest mm).

(ii) You realise that the top of the tank could be useful to line up egg-laying boxes for your chickens. Calculate the area of the top of the tank (in 2 and correct to two decimal places).