The answer
\(2.3 \times 10^{-2} \text{ m}^3\)
O-Level E-Math 2018 Paper 1 Question 11 · Verified worked solution by the Genius Plus Academy teaching team
What this question tests
This is Question 11 of the O-Level E-Math 2018 Paper 1. It tests volume scale factor = (length factor)³, in the Mensuration (similar solids) / standard form area. It is worth 3 marks. It is a worded / diagram-based question, so open your Ten-Year Series (TYS) or the official paper at this question, then follow our full worked solution below.
Lengths scale by \(\dfrac{1}{20}\), so volumes scale by \(\left(\dfrac{1}{20}\right)^3 = \dfrac{1}{8000}\). Model volume \(= \dfrac{184}{8000} = 0.023 \text{ m}^3 = 2.3 \times 10^{-2} \text{ m}^3\).
Answer: \(2.3 \times 10^{-2} \text{ m}^3\)
Same structure, different numbers
Swap the constants, dress a quadratic as a length, hide a derivative inside an integral, and a student sees a brand new problem. The structure underneath is the same, and so is the method. Once a student can name the structure, a whole row of questions that look different start to open the same way.
That is where marks really leak: in choosing the method, not in the algebra that follows. We call it Lock and Key, name the lock, then the key follows.
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Genius Plus Academy · O-Level & IP Mathematics
Our O-Level E-Math tuition trains the same recognise-the-structure method these worked solutions show, taught by a team that has marked these papers for years. It runs within our weekly Secondary Math programme, Sec 1 to 4 and IP.
It is a volume scale factor = (length factor)³ question from Mensuration (similar solids) / standard form, worth 3 marks.
Yes. IP (Integrated Programme) schools teach the same O-Level Mathematics content; they just sequence it differently and set their own internal exams, so these worked solutions apply to IP students too.
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