15.2 Plans and Elevations

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: drawing and reading the plan, front elevation and side elevation of 3D solids. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

• Understand what the plan, front elevation and side elevation of a solid are
• Draw plans and elevations of cuboids, prisms and solids made from cubes
• Work out a 3D solid from its plan and elevations
• Use measurements on plans and elevations to answer problems

Key words

• Plan: The view of a solid from directly above.
• Front elevation: The view of a solid from the front.
• Side elevation: The view of a solid from the side.
• Projection: A 2D drawing of a 3D solid seen from one direction.

Three views of a solid

Imagine looking at a solid straight on from one direction, with one eye closed. You see a flat 2D shape. The view from above is the plan. The views from the front and the side are the elevations.

Draw a line wherever there is an edge you can see, including edges where the solid steps forwards or backwards (or up or down in a plan). Plans and elevations on squared paper should be drawn to the same scale as the solid.

Worked example: reading the views above

Plan: a 3 by 2 rectangle. There are lines inside where the height changes, for example between the 1-cube-high front row and the taller back row.
Front elevation: 3 squares along the bottom, then 2 squares and 1 square stacked on the left. The line across shows the higher cubes are further back.
Side elevation: from the left, the back column is 3 cubes high and the front column is 1 cube high, so the view is an L shape.

Answer: plan 3 by 2, front elevation and side elevation both 3 units tall

Plans and elevations of common solids

• Cuboid; Plan rectangle; Front elevation rectangle; Side elevation rectangle
• Cylinder; Plan circle; Front elevation rectangle; Side elevation rectangle
• Cone; Plan circle with a dot in the centre; Front elevation triangle; Side elevation triangle
• Square-based pyramid; Plan square with both diagonals; Front elevation triangle; Side elevation triangle
• Sphere; Plan circle; Front elevation circle; Side elevation circle

Worked example: cuboid measurements

A cuboid is 6 cm long (front), 4 cm deep and 5 cm high. Give the size of each view.
Plan: length × depth = 6 cm by 4 cm.
Front elevation: length × height = 6 cm by 5 cm.
Side elevation: depth × height = 4 cm by 5 cm.

Answer: plan 6 × 4, front 6 × 5, side 4 × 5 (all in cm)

Key fact: The plan and the front elevation share the same width. The front and side elevations share the same height.

Using numbers on a plan

A plan of a solid made from cubes can show the number of cubes in each stack. Add the numbers to count the cubes. The biggest number in each column, looking from the front, gives the height of the front elevation there.

Worked example: counting from a plan

A plan is a 2 by 2 square. The numbers are 3 and 1 in the back row and 2 and 1 in the front row.
Total cubes = 3 + 1 + 2 + 1 = 7.
Front elevation heights: left column max(3, 2) = 3, right column max(1, 1) = 1.

Answer: 7 cubes; front elevation is 3 high on the left and 1 high on the right

From views back to a solid

To work out a solid from its views, start with the plan to see the shape of the base, then use the elevations to see the heights. Sketch it to check every view matches.

Worked example: naming a solid

Plan: a circle. Front elevation: a rectangle. Side elevation: a rectangle.
A circle from above and rectangles from the front and side means a circular cross-section that goes straight up.

Answer: a cylinder standing on one of its circular faces

Common mistakes

• Drawing the plan as a 3D sketch. Plans and elevations are flat 2D shapes.
• Leaving out lines where the solid steps back or changes height.
• Mixing up the front and side. Look for the arrows or labels on the diagram.
• Using the wrong measurements: the plan uses length and depth, not height.

Revision questions

Try these, then check your answers below each one.

Question 1. A cylinder stands on one of its circular faces. What is its plan view? (Choose from: A circle, A rectangle, A triangle, A square.)

Answer: A circle

Working: From above you see the circular top face, so the plan is a circle.

Question 2. A square-based pyramid stands on its base. What is its plan view? (Choose from: A square with both diagonals drawn, A triangle, A square with no lines inside, A circle with a dot in the centre.)

Answer: A square with both diagonals drawn

Working: The base outline is a square, and the four sloping edges appear as the diagonals meeting at the apex.

Question 3. A plan view of a solid made from cubes shows the number of cubes in each stack: 3, 1, 2 and 2. How many cubes are in the solid?

Answer: 8

Working: 3 + 1 + 2 + 2 = 8 cubes.

Related lessons

• Previous lesson: 15.1 3D Solids
• Next lesson: 15.3 Accurate Drawings 1
• In this chapter: 15.4 Scale Drawings and Maps
• In this chapter: 15.5 Accurate Drawings 2
• In this chapter: 15.6 Constructions

Continue in the full course

This lesson is section 15.2 (EGCMF1502) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.