2026 RSS P2 Q9

Secondary 4

11 marks

A team at EcoFlow Dynamics is designing a rainwater collection system to water its vegetable garden.

The diagram shows the roof that drains into the rainwater collection system.

The rectangular section shown by the dashed lines is not connected to the collection system.

Top-down view of roof

It is known that $1$ mm of rain falling on $1\text{ m}^2$ of roof produces $1$ litre of water.

During a heavy shower, $15$ mm of rain falls evenly on the roof.

Only $82\%$ of the rainwater falling on the collecting area is collected.

The vegetable garden requires 170 litres of water each day.

The tank must provide enough water for 5 consecutive days without rain.

For safety reasons, the amount of water in the tank must not exceed $90\%$ of its capacity.

The team has a total budget of $\$800$, which includes the cost of the tank and its installation.

Use $\pi=3.142$.

Tank	Shape and internal dimensions	Cost of tank	Installation cost
A	Cylinder of diameter $1.0$ m and height $1.1$ m	$\$620$	$\$130$
B	Cuboid of length $1.1$ m, width $1.0$ m and height $1.1$ m	$\$680$	$\$120$
C	Cylinder of diameter $1.2$ m and height $0.9$ m	$\$710$	$\$80$

Calculate the amount of water collected during the heavy shower.[4]
Using the information given and your answer to part (a), suggest a suitable tank for the rainwater collection system. Justify your decision with calculations.[7]

Solution:

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Answer:(a) $959.4$ litres (b) Tank C, $\$790$, stores up to $916.2072$ litres safely; divert excess water. Tank B ($\$800$) also works and retains all $959.4$ litres.

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Tank	Shape and internal dimensions	Cost of tank	Installation cost
A	Cylinder of diameter \(1.0\) m and height \(1.1\) m	\(\$620\)	\(\$130\)
B	Cuboid of length \(1.1\) m, width \(1.0\) m and height \(1.1\) m	\(\$680\)	\(\$120\)
C	Cylinder of diameter \(1.2\) m and height \(0.9\) m	\(\$710\)	\(\$80\)