GCSE · Perimeter, area & volume

Plans and elevations (views of 3D solids)Exam-style questions

Draw a 3D solid as three flat views: the plan from above, the front elevation and the side elevation. Draw each one square-on and true to size, use the lengths the views share (and the volume) to draw a missing view, see why a sloping face looks shorter than it is, record a model of cubes as a plan with numbers, explain the mistake in a wrong view, and work out the greatest and least number of cubes that two views allow.

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15 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 2Level 3Level 4
  1. 1
    The diagram shows a set of steps for a stage. The steps are a solid prism, and all three steps are the same size.30 cm40 cm1 mDiagram NOT accurately drawn

    Using a scale of 11 cm to 2020 cm, draw on a centimetre grid the side elevation of the steps, as seen in the direction of the arrow.

    (3 marks)
    Level 3 · 3 marksTry it
  2. 2
    Here is a square-based pyramid.

    The base is a square of side 44 cm. The top of the pyramid is directly above the centre of the base.4 cm4 cmNot to scale

    Asha is asked to draw the plan view of the pyramid. Here is her drawing.4 cmAsha's plan view(a) Describe the error Asha has made.

    (1 mark)
    (b) Using a one-centimetre grid, draw the correct plan view of the pyramid accurately.

    (2 marks)
    Level 3 · 3 marksTry it
  3. 3
    A door wedge is a prism. Its cross-section is a right-angled triangle.8 cm6 cm10 cm4 cmfrontsideDiagram NOT accurately drawn

    Ben looks at the wedge in the direction of the side arrow. He draws what he sees.4 cm10 cmBen's side elevation(a) What mistake has Ben made?

    (1 mark)
    (b) Draw the front elevation of the wedge accurately.

    (2 marks)
    Level 3 · 3 marksTry it
  4. 4
    A solid is made from centimetre cubes. Every cube stands on the table or on top of another cube.

    Here are the plan, the front elevation and the side elevation of the solid. The plan is drawn with the front of the solid at the bottom, and the side elevation is the view from the right.planfront elevationside elevationWork out the number of cubes in the solid.

    (2 marks)
    Level 3 · 2 marksTry it
  5. 5
    Here are the plan, the front elevation and the side elevation of a cuboid.7 cm3 cmplan7 cm2 cmfront elevation3 cm2 cmside elevationWork out the total surface area of the cuboid.

    (3 marks)
    Level 3 · 3 marksTry it

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