Isometric Projection Questions and Answers

Answer: A

Equal inclination means all three principal directions foreshorten by the same ratio, so one scale serves for every axis. Dimetric has two equal and trimetric three unequal ratios, which is why isometric is by far the commonest of the three in practice.

Answer: B

Three equal divisions of the full circle give 120 degrees between successive axes, which is what results when the three mutually perpendicular edges are equally inclined to the plane. Two axes are conventionally drawn at 30 degrees to the horizontal and the third vertical.

Answer: C

The two sloping axes are drawn at \( 30^{\circ} \) to the horizontal. That leaves the third axis vertical and separates the three by \[ 30^{\circ} + 90^{\circ} = 120^{\circ} \] which is the defining symmetry of isometric projection. It is also convenient in practice, since a thirty-sixty set square draws them directly without a protractor.

Answer: D

The top and the two visible sides each lie in one of the three isometric planes, and each carries its own ellipse orientation for circles drawn on it. Faces parallel to these three are treated the same way, whatever their position on the object.

Answer: A

Because each axis is equally inclined to the plane of projection, every true length is foreshortened by the same factor: \[ \text{isometric scale} = \sqrt{\tfrac{2}{3}} = \sqrt{0.6667} = 0.8165 \approx 0.816 \] Multiplying every true length by this produces a true isometric projection. Omitting it and using true lengths gives an isometric drawing, which is larger but far quicker to construct, and is what most drawing offices actually use.

Answer: B

Drawing with true lengths makes the figure larger than the projection by about 22.5 per cent, the reciprocal of 0.816. Since the shape and the proportions are unaffected, the drawing is what is normally made and the projection is reserved for cases where absolute size matters.

Answer: C

An isometric drawing uses true lengths where the projection uses foreshortened ones, so the size ratio is the reciprocal of the isometric scale: \[ \frac{1}{0.816} = 1.2247 \] \[ \text{excess} = 1.2247 - 1 = 0.2247 \approx 22.5\% \] So the drawing is a little over a fifth larger in every linear dimension. Areas differ by the square of that, \( 1.2247^{2} = 1.5 \), which is half again as much as the projection.

Answer: D

Isometric lines are foreshortened by the common ratio and so scale uniformly, whether the drawing uses true lengths or the isometric scale. A line oblique to all three axes foreshortens by a different amount and must be located from the ends of isometric lines instead.

Answer: A

Its ends are found by stepping off isometric distances in a box enclosing the feature, and the line is then joined between them. Measuring it directly is the commonest error and gives a figure that is wrong by an amount depending on its own inclination.

Answer: B

A box whose edges are isometric lines is drawn first and the object's features are located by offsets measured along those edges. It converts every non-isometric line into a pair of measurable isometric coordinates, which is why the method is so general.