A line drawn 20 cm long now measures 19.5 cm. The shrinkage factor is
Answer: C
Correct answer: 0.975
The shrinkage factor is the ratio of the present length to the original: \[ \frac{19.5}{20} = 0.975. \] It is less than one because the sheet has contracted, and being a ratio of two lengths it is dimensionless and can be applied directly to any other length on the same sheet.
Please log in or register to report this question.
A nominal scale of 1/1000 on a sheet with a shrinkage factor of 0.975 has a shrunk representative fraction of
Answer: D
Correct answer: 1/1026
Multiply the nominal fraction by the shrinkage factor: \[ \frac{1}{1000} \times 0.975 = \frac{0.975}{1000} = \frac{1}{1026}. \] Note the direction: the shrunk fraction is smaller than the nominal one, because after shrinkage a given drawing length stands for a greater actual length than it did.
Please log in or register to report this question.
An isometric drawing of a 100 mm edge is drawn, in true isometric projection, as
Answer: A
Correct answer: 81.6 mm
True isometric projection foreshortens every axis in the ratio \( \sqrt{2/3} = 0.816 \), so \[ 100 \times 0.816 = 81.6\ \mathrm{mm}. \] An isometric drawing, which is what is usually produced, ignores this and sets off the full 100 mm, giving a figure 22.5 per cent larger but identical in shape.
Please log in or register to report this question.
A drawing at 1:50 shows a rectangle 4 cm by 6 cm. The actual area represented is
Answer: B
The sides scale up to 200 cm and 300 cm, that is 2 m by 3 m, so the area is 6 square metres. Taking the drawn 4 by 6 as metres would give 24, and the area ratio is the square of the linear one rather than the linear one itself.
Please log in or register to report this question.
Halving the representative fraction of a drawing changes the area on the sheet by a factor of
Answer: C
Correct answer: one quarter
Halving the representative fraction halves every length on the sheet, and area goes as the square of length, so the drawing occupies a quarter of the area. This is why moving one step down the standard series is such a large change: 1:100 to 1:200 leaves the drawing at a quarter of the size, not half.
Please log in or register to report this question.
A plain scale of representative fraction 1/25 000 reading kilometres and hectometres to a maximum of 6 km must be
Answer: D
Correct answer: 24 cm long
\[ 6\ \mathrm{km} = 600\,000\ \mathrm{cm}, \qquad \frac{600\,000}{25\,000} = 24\ \mathrm{cm}. \] The scale is then divided into six main divisions of one kilometre each, and the first of those is subdivided into ten to read hectometres, with the zero placed at its right-hand end.
Please log in or register to report this question.
Match the scale with what it does.
1. Diagonal scale 2. Comparative scale 3. Scale of chords
P. Reads a length in two systems of units Q. Reads three successive units of one system R. Sets out and measures angles
Answer: A
Each construction answers a different need, and choosing the wrong one either loses precision or cannot make the reading at all. The diagonal scale is the workhorse for lengths and the chord scale the substitute for a protractor.
Please log in or register to report this question.
Match the scale class with its representative fraction.
1. Full size 2. Reducing 3. Enlarging
P. Less than unity Q. Exactly unity R. Greater than unity
Answer: B
Correct answer: 1-Q, 2-P, 3-R
The three classes are distinguished by where the representative fraction sits relative to one. Full size is exactly unity, drawing length equalling actual length. A reducing scale gives a fraction below unity, an enlarging scale one above. The classification follows directly from the definition of the fraction as drawing length over actual length.
Please log in or register to report this question.
Put the steps of constructing a plain scale in order.
1. Divide the first main division into subdivisions 2. Compute the length of scale from the fraction and maximum length 3. Determine the representative fraction 4. Divide the length into equal main divisions
Answer: C
Correct answer: 3, 2, 4, 1
Each step needs the one before it. Fix the representative fraction first, from what must fit on the sheet. Compute the length of scale from that fraction and the maximum length to be read. Divide that length into equal main divisions for the larger unit. Finally subdivide the first main division for the smaller unit, placing the zero at its right-hand end.
Please log in or register to report this question.
Consider the following statements about scales.
1. A diagonal scale reads three successive units 2. The isometric scale is 0.816 of the true scale 3. A shrunk representative fraction is larger than the nominal one
Answer: D
Correct answer: 1 and 2 only are correct
Statements 1 and 2 are correct: a diagonal scale reads three successive units, and the isometric ratio is 0.816. Statement 3 has the direction wrong - the shrunk fraction is obtained by multiplying by a factor less than one, so it is smaller than the nominal fraction, not larger.
Please log in or register to report this question.
