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O-Level E-Math · 2023 · P1 Q16 Congruence & similarity · Ratio of volumes of similar solids 1 mark · geometry & measurement (similar solids, reasoning) difficulty 2 of 5

O-Level E-Math 2023 Paper 1, Question 16: Ratio of volumes of similar solids

The answer

it makes sales look about 27 times larger, not 3 times

O-Level E-Math 2023 Paper 1 Question 16 · Verified worked solution by the Genius Plus Academy teaching team

What this question tests

This is Question 16 of the O-Level E-Math 2023 Paper 1. It tests ratio of volumes of similar solids, in the Congruence & similarity area. It is worth 1 mark. 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.

Step-by-step solution

Because the tins are geometrically similar with a length scale factor of 3, their volumes are in the ratio \(3^3 = 27 : 1\). The 2020 tin therefore looks 27 times bigger, suggesting sales rose roughly 27-fold, which greatly exaggerates the stated tripling.

Answer: it makes sales look about 27 times larger, not 3 times

Same structure, different numbers

A question is hard because of its structure, not its surface.

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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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.

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What does O-Level E-Math 2023 Paper 1 Question 16 test?

It is a ratio of volumes of similar solids question from Congruence & similarity, worth 1 mark.

Is this the same as IP Math?

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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