Scale and scale factors, ratio and proportion, area and volume calculations, the effect of scale factor on area and volume, tolerances and limits, and reading and interpreting dimensioned drawings and data, with units carried through.

A focused answer to Eduqas A-Level Product Design on scale, ratio and tolerancing maths: scale factors and ratio, area and volume calculations, how a scale factor affects area and volume, tolerances and upper and lower limits, and reading dimensioned drawings, with worked examples.

Generated by Claude Opus 4.812 min answerUpdated 2026-06-02

Reviewed by: AI editorial process; not yet individually human-reviewed

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What this dot point is asking
Scale and scale factors
Ratio, area and volume
How scale factor affects area and volume
Tolerances, limits and reading drawings

What this dot point is asking

Eduqas wants you to calculate scale and scale factors, use ratio and proportion, find areas and volumes, understand how a scale factor affects area and volume, work with tolerances and limits, and read dimensioned drawings. This is the geometric maths of the paper, with a calculator allowed and units carrying marks, and the square and cube scaling of area and volume is one of the most-tested ideas.

Scale and scale factors

Ratio, area and volume

How scale factor affects area and volume

Tolerances, limits and reading drawings

A tolerance is the permitted variation in a dimension, giving an upper limit (the basic size plus the tolerance) and a lower limit (the basic size minus the tolerance); any part between the limits is acceptable, and the tolerance is the difference between them. For $40 \pm 0.2$ mm the limits are $39.8$ mm and $40.2$ mm. Tolerances may be bilateral (plus and minus) or unilateral (one direction). Reading a dimensioned drawing means interpreting the scale, the dimensions and units, the tolerances, and any datums the dimensions are measured from, and being able to scale a measured length up or down to the real size. These skills connect the maths to manufacture (quality control and tolerances) and to communication (working drawings), and they are tested both as calculations and as the basis for a costing or quantity problem.

Applying scale factor to area, volume and mass

Scale the length

A prototype box has a side of $50$ mm and is scaled up by a linear scale factor of $k = 2$ for the final product. The new side length is $50 \times 2 = 100$ mm.

Scale the area

Surface area scales by $k^2 = 2^2 = 4$ . So if the prototype's surface area was, say, $15\,000$ square mm, the product's is $15\,000 \times 4 = 60\,000$ square mm. More material (and cost) than the doubling of length suggests.

Scale the volume and mass

Volume scales by $k^3 = 2^3 = 8$ . So the product's volume (and, at the same density, its mass) is eight times the prototype's. A part that felt light at model size could be heavy at full size.

State the design consequence

Conclude that scaling a design up multiplies area by 4 and volume and mass by 8 for a doubling of length, so material use, weight and cost rise steeply. State the $k$ , $k^2$ and $k^3$ relationships and keep the units (mm, square mm, cubic mm), because they are the marked ideas.

Exam-style practice questions

Practice questions written in the style of WJEC Eduqas exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

Eduqas 20204 marksA drawing is at a scale of 1:5. A feature measures 30 mm on the drawing. Calculate the real size of the feature, and state the real size if the scale were 2:1 instead.

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A Component 1 scale calculation. Marks for each conversion.

At a scale of 1:5, the real object is five times the drawing, so the real size is $30 \times 5 = 150$ mm. At a scale of 2:1, the drawing is twice the real object (an enlargement), so the real size is half the drawing: $\frac{30}{2} = 15$ mm.

Award marks for $150$ mm and $15$ mm. A common dropped mark is multiplying when the scale is an enlargement (2:1) instead of dividing. Read the scale as drawing:real, so 1:5 means divide the real by 5 to draw it, and multiply the drawing by 5 to get the real size.

Eduqas 20226 marksA cube of side 20 mm is scaled up by a linear scale factor of 3. Calculate the new side length, the ratio of the new surface area to the old, and the ratio of the new volume to the old. Explain why area and volume do not scale by the same factor as length.

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A Component 1 scale-factor calculation. Marks for the length, the area ratio, the volume ratio and the explanation.

New side length $= 20 \times 3 = 60$ mm. Area scales by the square of the linear scale factor: $3^2 = 9$ , so the new surface area is 9 times the old. Volume scales by the cube of the linear scale factor: $3^3 = 27$ , so the new volume is 27 times the old.

Area and volume do not scale by the same factor as length because area is a product of two lengths (so it scales by the factor squared) and volume is a product of three lengths (so it scales by the factor cubed). A top answer gives $60$ mm, $9$ and $27$ and explains the square and cube relationship, which is a favourite exam point (a part scaled up gets heavy and costly fast).

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Sources & how we know this

Eduqas A Level Design and Technology specification (Product Design) — Eduqas (2017)