Question 2 of 10: Isometric Pictorial from an Orthographic Projection

Question 2: Isometric Pictorial from an Orthographic Projection (10 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. The front view is a rectangle with a 45° diagonal line running from the lower-left toward the upper-right corner (a chamfer/cut-corner plane) and a hidden (dashed) rectangle inside it, indicating a rectangular slot that does not break the front silhouette. The top and side views confirm the object is a two-tier stepped rectangular block: a lower full-width/full-depth base and an upper, narrower plate that carries the slot and the 45° corner cut.

Find. A single isometric pictorial (freehand, no straight edge) that shows the block's step, the 45° chamfered corner, and the hidden slot in one 3-D view.

Approach. Isometric axes are drawn at 120° to one another — one vertical and the other two at 30° above the horizontal to either side — so that all three principal dimensions (width, depth, height) can be laid off to true (isometric) scale along those three axes with no distortion between them; angled/inclined true-length lines (like the 45° chamfer) are NOT drawn at their true angle in isometric — they are plotted by locating their two end points from box coordinates and connecting them (the "box construction" method), never by protracting the angle directly.

1. Block in the enclosing box. Lightly sketch a rectangular box along the three isometric axes using the overall width, depth, and height read off the three given views.
2. Locate the chamfer end points on the box, not the angle. From the front view, the 45° line runs from one top corner partway along the top edge; measure those two distances along the appropriate isometric edges and connect the two points with a straight line — this reproduces the true corner cut without ever sketching "45°" directly in the isometric.
3. Add the step. Drop the height of the lower tier down from the box's base plane and draw its own smaller enclosing box, sharing the isometric axis directions.
4. Add the slot as hidden detail. Locate the slot's two end edges on the top face using box coordinates, and draw them as parallel hidden (dashed) lines running the slot's depth, since the slot does not break through to a visible face in this pictorial orientation.
5. Darken visible edges; leave true hidden edges dashed or omit per sketch convention (pictorial sketches commonly show only what materially helps read the shape — the rubric rewards correct angles of the isometric axes and correct projection, not exhaustive hidden-line detail).