The isometric scale bears to the true scale the ratio
Answer: A
Edges inclined equally to the three axes are foreshortened in that proportion, which is the square root of two thirds. Drawing with true lengths instead gives an isometric drawing rather than a true isometric projection.
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An isometric drawing differs from an isometric projection in using
Answer: B
Correct answer: true lengths rather than foreshortened ones
A true isometric projection foreshortens all three axes to 0.816 of their real length. An isometric drawing dispenses with that and sets off true lengths along the axes, so the figure is about 22 per cent larger than the projection but identical in shape and far easier to construct - which is why it is what is almost always drawn.
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Preferred standard scales for engineering drawings are chosen so that
Answer: C
Correct answer: the ratio is a simple multiple of 1, 2 or 5
Standard scales run 1:1, 1:2, 1:5, 1:10, 1:20, 1:50 and so on, so that the mental arithmetic of converting a scaled length is easy and a familiar set of scale rules serves every drawing. An arbitrary ratio such as 1:37 would be correct but would need a scale constructed specially and computation at every reading.
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A drawing marked NTS indicates that it is
Answer: D
Correct answer: not to scale, so no dimension may be measured from it
NTS warns that the geometry on the sheet does not correspond to the object in any consistent proportion, so nothing may be scaled from it and every dimension needed must be written on. It is used for diagrammatic and schematic drawings, and for details deliberately distorted to show a thin feature clearly.
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A scale on which 1 cm represents 5 m has a representative fraction of
Answer: A
Five metres is 500 centimetres, so the ratio of drawing length to actual length is one in five hundred. Converting both lengths to the same unit before forming the ratio is the step most often omitted in this calculation.
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At a representative fraction of 1/25 000, one centimetre on the drawing stands for
Answer: B
Correct answer: 250 m
At 1/25 000 the drawing length is one twenty-five-thousandth of the real one, so \[ 1\ \mathrm{cm} \rightarrow 25\,000\ \mathrm{cm} = 250\ \mathrm{m}. \] The conversion from centimetres to metres is where the arithmetic usually goes wrong; keeping both lengths in centimetres until the last step avoids it.
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A scale of representative fraction 1/500 to read a maximum of 60 m must be constructed to a length of
Answer: C
Correct answer: 12 cm
The length of scale is the maximum length multiplied by the representative fraction, both in the same units: \[ 60\ \mathrm{m} = 6000\ \mathrm{cm}, \qquad \frac{6000}{500} = 12\ \mathrm{cm}. \] A convenient result - a scale much longer than about 30 cm becomes awkward to use, which is one practical check on the choice of representative fraction.
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A scale 15 cm long has been constructed to read a maximum of 6 m. Its representative fraction is
Answer: D
Correct answer: 1/40
The representative fraction is the drawing length over the actual length in the same units: \[ \frac{15\ \mathrm{cm}}{600\ \mathrm{cm}} = \frac{1}{40}. \] Forgetting to convert the 6 m to centimetres gives 1/0.4, and inverting the ratio gives 40, both of which are dimensionally impossible for a reducing scale.
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A vernier with 10 divisions occupying 9 main scale divisions of 1 mm each has a least count of
Answer: A
Correct answer: 0.1 mm
The least count is the difference between one main division and one vernier division. Ten vernier divisions occupy nine main divisions, so each vernier division is 0.9 mm and \[ 1.0 - 0.9 = 0.1\ \mathrm{mm}. \] Equivalently, the least count is the main division divided by the number of vernier divisions, which is the quicker form to use.
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To achieve a least count of 0.02 mm from a main scale divided into 0.5 mm, the vernier must carry
Answer: B
Correct answer: 25 divisions
The least count is the main scale division divided by the number of vernier divisions: \[ n = \frac{0.5}{0.02} = 25. \] So 25 vernier divisions are made to span 24 main divisions, which is the standard construction of a metric caliper reading to two hundredths of a millimetre.
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