Combining two solids

The essentials

To draw two solids placed centrally, start with the lower solid. Draw its top face and find the centre by drawing its diagonals (or the centre of the ellipse for a circular face). This point is where the common vertical axis passes. Draw the base of the upper solid on this top face with the same centre and with its sides in the required orientation, then raise its height along the vertical axis using the isometric scale. Finally, darken the visible outlines and erase the construction lines.

Key points

• Common axis: both solids share one vertical axis when placed centrally with axes not parallel to the HP.
• Total height = height of lower solid + height of upper solid, both foreshortened. Example: a 50 mm cube with a 40 mm high cone on it gives an apex height of 90 × 0.816 ≈ 73.5 mm in isometric projection.
• When a sphere rests centrally on a solid, its centre is located one isometric radius above the top surface, while its outline is drawn with the true radius.
• If the upper solid is smaller, part of the top face of the lower solid stays visible; if larger, it overhangs and hides part of the lower solid's edges.
• Orientation: a hexagonal or square upper base may have its sides parallel or perpendicular to the VP independently of the lower solid.

Exam tips

• Keep a light thin-line box for each solid; it makes alignment of centres easy.
• Check that every height on the drawing has been read from the isometric scale.

Common mistakes

• Placing the upper solid at a corner of the lower one instead of at its centre.
• Measuring the combined height in full size.
• Drawing hidden edges of the lower solid that are covered by the upper solid.