Isometric Projection Questions and Answers

Answer: A

Correct answer: 60 mm

An isometric *drawing* is set out with true lengths along the isometric axes, so a 60 mm edge is drawn 60 mm. That is the whole convenience of the method: the given dimensions are used directly with no scale conversion. The result is about 22 per cent larger than the true projection would be, which is accepted because the shape and proportions are identical.

Answer: B

Correct answer: 49 mm

A true isometric *projection* foreshortens every isometric line by \[ \sqrt{2/3} = 0.8165, \] so \( 60 \times 0.8165 = 49 \) mm. That is the length an actual orthographic projection onto the isometric plane would produce, and drawing it requires a special isometric scale - which is precisely the trouble the isometric drawing avoids.

Answer: A

An isometric drawing is set out with true lengths, so it comes out larger than the true isometric projection by the reciprocal of the isometric scale, \[ \frac{1}{0.816} \;=\; 1.225. \]

In the projection the major axis of the ellipse equals the circle's own diameter, so in the drawing it is that diameter enlarged by the same factor:

\[ \text{major axis} \;=\; 1.225\,d \;=\; 1.225 \times 50 \;=\; 61.25 \;\approx\; 61.3\ \mathrm{mm}. \]

The 50 mm offered as a distractor is the major axis of the true isometric projection, and 40.8 mm is 50 mm wrongly reduced by the 0.816 scale instead of enlarged by its reciprocal.

Answer: B

The minor axis of an isometric ellipse is a fixed fraction of the major axis, the ratio being \[ \frac{\text{minor}}{\text{major}} \;=\; \frac{1}{\sqrt{3}} \;=\; 0.577. \]

The major axis of the drawing was 61.25 mm, so

\[ \text{minor axis} \;=\; 0.577 \times 61.25 \;=\; 35.36 \;\approx\; 35.4\ \mathrm{mm}, \]

which is the circle's diameter times \( 0.707 \):

\[ 0.707 \times 50 \;=\; 35.4\ \mathrm{mm}. \]

The 28.9 mm offered as a distractor is \( 0.577 \times 50 \), the minor axis belonging to the true isometric projection rather than to the drawing.

Answer: A

The ratio follows from the 30 degree inclination of the isometric planes and is the same on all three of them. It is what makes a single ellipse template usable throughout an isometric drawing, provided the orientation is correct.

Answer: B

Correct answer: 40 mm

In an isometric drawing every edge parallel to an isometric axis is set out at its true length, so the enclosing box carries 80, 60 and 40 mm on the three axes and the vertical edge is 40 mm. The box is drawn first and the object developed within it, which is the standard method for anything whose faces are not all rectangular.

Answer: C

Being parallel to none of the three axes, it foreshortens by an amount that depends on its own direction rather than by the common ratio. Its ends must be fixed from isometric measurements and the line then drawn between them.

Answer: D

The three isometric planes present a right angle as either 60 or 120 degrees according to the orientation of the corner within the plane. Both distortions occur in the same drawing, which is why no angle on it may be measured.

Answer: A

A sphere presents the same circular silhouette from every direction, so no foreshortening applies to it: \[ d_{drawn} = d_{true} = 70 \ \mathrm{mm} \] It is the single case in which the isometric projection and the isometric drawing are identical in size. Applying the 0.816 scale would wrongly give \( 70 \times 0.816 = 57.1 \) mm, which is offered as a distractor.

Answer: B

Cabinet oblique halves the receding dimension by definition: \[ d_{drawn} = \tfrac{1}{2} \times 60 = 30 \ \mathrm{mm} \] This counteracts the exaggerated depth that cavalier projection produces, since cavalier draws the receding dimension full size at \( 60 \) mm and looks unnaturally deep. The frontal face is unaffected in both forms and keeps its true shape and size.