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.

Start practising Read the lesson

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

DifficultyAllLevel 2Level 3Level 4
  1. 1
    Kate is going to fill a raised flower bed with soil.

    The flower bed is a prism with two levels. The diagrams show its front elevation and its side elevation. The side elevation is its cross-section.150 cm50 cmfront elevation40 cm40 cm50 cm20 cmside elevationfrontbackDiagram NOT accurately drawn

    Soil is sold in bags of 4040 litres.

    Kate buys 1010 bags of soil.

    11 litre =1000= 1000 cm³

    Does Kate buy enough soil to fill the flower bed?

    You must show how you get your answer.

    (5 marks)
    Level 4 · 5 marksTry it
  2. 2
    Kemi makes a solid from centimetre cubes. Every cube stands on the table or on top of another cube.

    Here are the front elevation and the side elevation of the solid. The side elevation is the view from the right.6 cm2 cm2 cm4 cm3 cm3 cm1 cm4 cmfront elevationside elevationNot drawn accurately

    Work out the greatest number of cubes Kemi could have used, and the least number she could have used.

    You must show your working.

    (3 marks)
    Level 4 · 3 marksTry it
  3. 3
    Ana wants to make a solid from centimetre cubes. Every cube must stand on the table or on top of another cube.

    The solid must have this front elevation and this side elevation. The side elevation is the view from the right.front elevationside elevationAna saysI can make this solid using exactly 1212 cubes.Is Ana correct? Show how you decide.

    (4 marks)
    Level 4 · 4 marksTry it
  4. 4
    A box is a cuboid. The plan of the box is a square.

    The area of the front elevation of the box is 2020 cm²

    The volume of the box is 100100 cm³

    Work out the total surface area of the box.

    You must show your working.

    (4 marks)
    Level 4 · 4 marksTry it
  5. 5
    A tent is in the shape of a pyramid with a rectangular base.

    The base is 2.42.4 m long and 1.81.8 m wide. The top of the tent is directly above the centre of the base, and each sloping edge is 1.71.7 m long.2.4 m1.8 m1.7 mNot to scale
    (a) Using a scale of 11 cm to 3030 cm, draw the plan view of the tent on a one-centimetre grid.

    (2 marks)
    (b) Show that the height of the tent is 8080 cm.

    (4 marks)
    (c) Work out the volume of the tent. Give your answer in m³.

    [The volume of a pyramid is 13×\frac{1}{3} \times area of base ×\times perpendicular height.]

    (2 marks)
    Level 4 · 8 marksTry it