Scales Questions and Answers

Answer: A

Angles require a scale of chords or a protractor, since the diagonal construction divides lengths rather than arcs. The other three are all sets of three successive linear units, which is precisely what a diagonal scale reads.

Answer: B

Correct answer: measuring an angle with a scale of chords

A scale of chords works from a circle of a chosen radius and gives angles directly; the representative fraction of the drawing plays no part in it, which is why the same scale of chords serves drawings at any scale. The other three all involve converting between drawing and actual lengths, which is precisely what the fraction is for.

Answer: C

Correct answer: understated by about ten per cent

Every length on the copy is 90 per cent of what it was, so measuring the copy with a rule graduated for the original scale gives a figure about a tenth too small. The error is systematic and invisible - nothing on the copy reveals that it has been reduced - which is exactly why written dimensions govern over scaled ones.

Answer: D

Correct answer: understated, and must be corrected upward

A stretched chain covers more ground per nominal length, so fewer chain lengths are counted over a given distance and the recorded figure is too small. The correction is to multiply by the ratio of true to nominal length, here 20.1/20, which increases the recorded distance by half a per cent. Using the chain consistently does not help, since every measurement is wrong by the same proportion.

Answer: A

Correct answer: both the assertion and the reason are true and the reason explains the assertion

Both are true and the reason is the justification. Photocopying, printing at another sheet size, scanning and the ordinary movement of paper with humidity all change the lengths on a drawing, and none of them leaves any trace. The written dimension is unaffected by all of it, which is why it governs and why scaling from a drawing is a last resort.

Answer: B

Correct answer: the assertion is false although the reason offered is a true statement in itself

The reason is true - the sheet has contracted - but the arithmetic in the assertion is inverted. The shrunk fraction is obtained by multiplying by the shrinkage factor, which is less than one, so the fraction becomes smaller: 1/1000 at a factor of 0.975 gives about 1/1026. Dividing would make it larger, which is the wrong direction.

Answer: C

Correct answer: resolves finer but must be made and read with more care

The vernier obtains its resolution from the difference between two nearly equal divisions rather than from subdividing a line, so it can read finer than a diagonal scale of the same size. The cost is precision of construction and care in reading: the coincidence of lines must be judged correctly, and a misjudgement gives a wrong answer that looks perfectly definite.

Answer: D

Correct answer: the maximum length the scale must read

The length of scale is the maximum length to be read multiplied by the representative fraction, so those two quantities alone determine it. The number of subdivisions affects how the constructed length is divided but not how long it is, the sheet size limits what is practicable rather than entering the calculation, and the manufacturing units are irrelevant.