Cone, cylinder, sphere and hemisphere

The essentials

Curved solids are drawn using ellipses. A circle lying on a face parallel to an isometric plane appears as an ellipse. In school drawing this ellipse is drawn by the four-centre method: draw the isometric square (rhombus) that encloses the circle, using the isometric length of the diameter as its side; join the corners at the obtuse angles to the midpoints of the opposite sides; the points where these lines meet, together with the obtuse corners, give four centres for four arcs that make the approximate ellipse.

Key points

• Cylinder: draw ellipses for both ends along the axis and join them with two common tangents parallel to the axis.
• Cone: draw the base ellipse, locate the apex on the axis at the isometric height, and draw tangents from the apex to the ellipse.
• Sphere: in isometric projection it appears as a circle whose radius equals the TRUE radius of the sphere. This is because the point of the sphere farthest from the centre in any direction is always at the true radius.
• Locating a sphere: its centre is found by drawing an ellipse (isometric circle) through which the centre is raised by the isometric length of the radius.
• Hemisphere on its flat face: the flat face is an ellipse drawn with isometric dimensions, and the curved surface is an arc of true radius drawn from the same centre.
• Exact ellipse in isometric projection: major axis = true diameter, minor axis ≈ 0.577 × true diameter.

Exam tips

• Mark the centre of every ellipse and the direction of the axis before drawing arcs.
• For a hemisphere, show the junction of the curved outline and the flat elliptical face neatly.

Common mistakes

• Drawing the sphere with the isometric (reduced) radius.
• Drawing ellipses free-hand without first constructing the rhombus.
• Making the generators of a cone touch the ellipse at the wrong points; they must be tangents.