Geometry · GCSE Maths
Plans and elevations
GCSE Maths plans and elevations: draw front, side and plan views of 3D solids, read hidden detail as dashed lines, and match sketches to objects.
Plan is bird’s-eye (from above). Front and side elevations are side views. Dashed lines show hidden edges behind the solid.
The important bits
What you need to know
- 1
A plan is the view from directly above — bird’s-eye. It shows the footprint of the solid on the horizontal plane.
- 2
A front elevation is the view from the front. A side elevation is from the left or right — read which side the question names.
- 3
Hidden edges that would not be visible in a real view are shown as dashed lines in textbook diagrams.
- 4
For a solid on a square base with a central peak, the plan may show a square; front and side elevations show triangles or rectangles.
- 5
A cylinder: plan is a circle (or rectangle if drawn in 2D layout); front elevation is a rectangle width = diameter, height = cylinder height.
- 6
Drawing from a 3D diagram: sketch three separate 2D views, aligned so widths match (plan width = front width).
- 7
From three views, reconstruct the 3D shape by imagining how the views lock together — exam questions ask which sketch matches.
- 8
Scale and grid: count squares on the provided grid. One square may represent 1 cm; label if the question gives a scale.
Quotations worth analysing
Short evidence. Real method.
“Plan view from above”
Students who draw the front view as the plan have rotated the object wrong. Plan has no vertical height — only footprint.
“Dashed lines for hidden edges”
Solid lines for visible edges. Hidden edges behind the solid are dashed. Missing dashes lose accuracy marks on full drawings.
“Widths must align across views”
Front width equals plan width. Side depth equals plan depth. Misaligned views cannot come from one solid.
Go deeper
Prism on a rectangular base
A cuboid 4 cm by 3 cm by 2 cm (length 4, width 3, height 2). Plan (from above): rectangle 4 by 3. Front elevation (face 4 wide, 2 high): rectangle 4 by 2. Side elevation (face 3 wide, 2 high): rectangle 3 by 2. Hidden edges on the plan none if solid block. A hollow box open at top: plan shows outer rectangle, dashed inner rectangle for the hidden bottom inside walls if drawn in section style — GCSE usually uses simple solids. L-shaped prism: plan is the L footprint; elevations show the step height. Count grid squares for each view.
Go deeper
Cylinder and cone
Cylinder radius 2 cm, height 5 cm. Plan: circle diameter 4 (or circle on grid). Front elevation: rectangle width 4, height 5. Side elevation: same rectangle. Cone on base radius 2, height 6: plan circle diameter 4; front elevation triangle base 4 height 6; side elevation same triangle. Sphere: plan and elevations are circles diameter equal to sphere — unusual at GCSE but possible as “circle of maximum width”. Composite solids: draw views of the combined outline — a hemisphere on a cylinder shows rectangle plus semicircle on top in elevation.
Go deeper
Matching views to objects
Given three views, eliminate options that disagree. If the plan is a circle but front elevation is a triangle, think cone. If plan is square and front is rectangle, cuboid. If plan has a hole (dashed inner square), hollow prism. Work systematically: compare plan footprint to each option’s base. Then check front height profile. GCSE multiple-choice often shows four sketches; one matches all three views. Trace each view mentally onto the options. A common trap: correct plan and front but wrong side depth — side elevation width must equal plan depth.
See the idea in action
A square-based pyramid: base 4 cm square, height 6 cm. Plan: square 4 by 4 (footprint). Front elevation: triangle base 4 cm, height 6 cm (apex above centre of base). Side elevation: triangle base 4 cm, height 6 cm (same as front for a regular square pyramid). Hidden base edges on elevations may be dashed if the base line is behind the sloping faces in some orientations; textbook front view often shows solid base.
Exam technique
Turn knowledge into marks
Draw three separate views on the grid provided. Align widths and depths. Use dashed lines for any hidden edge the mark scheme expects.
Common mistakes
Do not give these marks away
- 01
Drawing the front view instead of the plan when asked for a bird’s-eye view.
- 02
Side elevation width not matching the plan depth.
- 03
Omitting dashed lines for hidden edges on hollow or composite solids.
Which view of a 3D solid is drawn from directly above?
AFront elevation
BSide elevation
CPlan
DIsometric
Show the answer
Plan. The plan is the bird’s-eye view showing footprint. Elevations are side views. Isometric is a 3D-style drawing, not an orthographic view.
Quick questions
If this is the bit you searched
What is the difference between plan and elevation?
Plan is from above showing footprint. Elevations are side views from the front or side showing height and width or depth and height.
When do I use dashed lines?
For edges hidden behind the solid that would not be visible in a true orthographic view. Convention on GCSE diagrams.
How do I draw a cylinder plan?
A circle with the same diameter as the cylinder, seen from above. Front and side elevations are rectangles.
What if front and side elevations look the same?
Common for symmetric solids (cube, square pyramid, cylinder). Different views are still required; they may coincide.