Surface developments, true shapes & intersections
Graphic Communication · Higher · mrkellydt.co.uk
What you're learning in this topic
Learning intention WALT
We are learning about surface developments, true shapes & intersections, specifically to:
know
- correct surface developments of prisms, cylinders, pyramids and cones
understand
- common geometric forms with single cuts
- interpenetration and intersections of prisms and cylinders
Success criteria WILF
- I can identify correct surface developments of prisms, cylinders, pyramids and cones
- I can interpret common geometric forms with single cuts
- I can describe interpenetration and intersections of prisms and cylinders
Surface developments
A surface development (a net) is the flat shape that folds up to make a 3D form. Packaging is designed this way.
- Prism: a row of rectangles plus the two end shapes.
- Cylinder: a rectangle whose length is the circumference (π × diameter) plus two circles.
- Cone: a sector of a circle whose radius is the slant height.
- Pyramid: triangles whose sloping edges are drawn true length.
- When a form is cut at an angle, the development shows the cut line traced around the surface. Exam questions show several nets and ask which is correct: check the order of faces and where the cut falls.
Developments use fold lines and often glue tabs. To reduce waste and cost, nets are nested together on the sheet.
Shapes, forms and cuts
Forms you should recognise in any view: squares, rectangles, circles, hexagons and octagons; prisms, pyramids, cones and cylinders. Questions combine two forms or show a single cut (e.g. a cylinder cut at an angle gives an ellipse as the true shape).
Interpenetration and intersections HIGHER
When two solids join, such as a pipe meeting another pipe or a cylinder through a prism, the line where their surfaces meet is the line of intersection. It is found by dividing one form into strips (generators), projecting where each line meets the other surface into the other views, and joining the points with a smooth curve. Equal cylinders meeting at 90° give straight-line intersections in the elevation. The true shape of an oblique cut through a cylinder is an ellipse.
Key terms
| Surface development | The flat net that folds to make a 3D form. |
|---|---|
| Cylinder development | Rectangle of length π × d, plus two circles. |
| Cone development | A sector with radius equal to the slant height. |
| Glue tab | Extra flap on a net to join edges. |
| Line of intersection | The line where two joined solids' surfaces meet. |
| True shape of an angled cut through a cylinder | An ellipse. |
Quick check
1. The length of a cylinder's development is…
- The diameter
- The radius
- π × diameter
- 2 × height
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2. A cone develops into…
- A long rectangle
- A complete circle
- An equilateral triangle
- A sector of a circle
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3. Fitting as many nets as possible onto a sheet…
- Reduces waste and cost
- Increases waste
- Makes folding harder
- Is not allowed
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4. A cylinder cut at an angle has a true shape that is…
- A circle
- An ellipse
- A rectangle
- A parabola
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Printable worksheet
An I do, we do, you do worksheet for this topic, with a separate answer sheet.