ESAT Maths 1 · free worked solution

ESAT Maths 1 similar solids: cube the scale factor

Similarity solution: cube the length scale factor to find the larger solid's volume, 135 cm³.

Similarity and volume scale factorsSpecification M3.10Reviewed 5 August 2026

Answer first

Option C

The correct answer is

135 cm3135\,\text{cm}^3

Lengths, areas and volumes scale by different powers: volume needs the cube of the length factor.

This is original UniGenius practice material from the reviewed Maths 1 bank. It is not an official UAT-UK question, past paper, or recalled question.

The question

Read the setup, then choose the shortest valid route

Two similar solids have a length scale factor of 2:32:3 from smaller to larger. The smaller volume is 40 cm340\,\text{cm}^3. What is the larger volume?

  • A60 cm360\,\text{cm}^3
  • B90 cm390\,\text{cm}^3
  • C135 cm3135\,\text{cm}^3Answer
  • D180 cm3180\,\text{cm}^3
  • E270 cm3270\,\text{cm}^3

Worked solution

The route in 2 steps

  1. Volumes scale as the cube of the length factor: (3/2)3=27/8(3/2)^3=27/8.

  2. The larger volume is 40×27/8=135 cm340\times27/8=135\,\text{cm}^3.

Next action

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