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G13

Construct and interpret plans and elevations of 3D shapes

Plans and elevations

Worked answers, methods and verified real exam appearances for G13 on Edexcel GCSE Maths 1MA1.

Explanation

  • A plan is the view from directly above. A front or side elevation is an orthographic view from the named horizontal direction, drawn without perspective.
  • Corresponding widths align between the plan and front elevation; depths align between the plan and side elevation. For stacks of unit cubes, a numbered plan records the height in each occupied cell.
  • An elevation shows, for each viewing column, the greatest height visible along the line of sight.
  • Use true lengths in the viewing plane and include changes of outline, but do not add hidden internal edges unless requested.
  • Examiners compare dimensions and visible column heights, not artistic realism.
A numbered plan projects to the greatest visible height in each elevation column.

Worked example

A cuboid measures 77 cm long, 44 cm deep and 33 cm high. State the dimensions of its plan, front elevation looking along the depth, and side elevation.

  1. 1.The plan shows length and depth, so it is 77 cm by 44 cm.
  2. 2.Looking along the depth, the front elevation shows length and height: 77 cm by 33 cm.
  3. 3.The side elevation shows depth and height: 44 cm by 33 cm.

Answer: Plan 7×47\times4 cm; front elevation 7×37\times3 cm; side elevation 4×34\times3 cm.

Common mistakes

  • Don't include the height in the plan even though the plan is viewed from above.
  • Don't add all stack heights along a line of sight instead of taking the greatest visible height.

Exam tip

Before drawing an elevation, write the two dimensions visible from that direction and project matching corners with straight construction lines.

Worked practice

Q1
Tier 1 · Easy

1

A cuboid is 88 cm long, 55 cm wide and 33 cm high. State the shape and dimensions of its plan.

(2)

(Total for Question 1 is 2 marks)

Mark scheme

Mark scheme for question 1
QuestionAnswerMarkMark scheme
1
  • A rectangle 88 cm by 55 cm
2The plan is viewed from above, so it shows length and width but not height. Therefore it is an 88 cm by 55 cm rectangle.
Q2
Tier 2 · Standard

2

A numbered plan of unit-cube stacks has two rows. From north to south, the rows are (2,1)(2,1) and (3,0)(3,0), with entries ordered west to east. Give the visible column heights in the front elevation viewed from the south and in the side elevation viewed from the east.

(3)

(Total for Question 2 is 3 marks)

Mark scheme

Mark scheme for question 2
QuestionAnswerMarkMark scheme
2
  • Front elevation, west to east: (3,1)(3,1)
  • Side elevation, north to south: (2,3)(2,3)
3From the south, take the greatest height in each west-east column: west gives max⁡(2,3)=3\max(2,3)=3 and east gives max⁡(1,0)=1\max(1,0)=1. From the east, take the greatest height in each north-south row: north gives max⁡(2,1)=2\max(2,1)=2 and south gives max⁡(3,0)=3\max(3,0)=3.
Q3
Tier 3 · Hard

3

A solid uses vertical stacks of unit cubes on all four cells of a 22 by 22 plan. Its front elevation viewed from the south has heights (3,2)(3,2) from west to east. Its side elevation viewed from the east has heights (2,3)(2,3) from north to south. Find the least possible number of cubes and give one numbered plan that achieves it.

(4)

(Total for Question 3 is 4 marks)

Mark scheme

Mark scheme for question 3
QuestionAnswerMarkMark scheme
3
  • 77 cubes; for example, from north to south the plan rows can be (1,2)(1,2) and (3,1)(3,1), with entries west to east.
4The height 33 required in both the west front column and south side row can be placed in the south-west cell. The height 22 required in both the east front column and north side row can be placed in the north-east cell. The other two occupied cells need at least one cube each, giving 3+2+1+1=73+2+1+1=7. The plan rows (1,2)(1,2) and (3,1)(3,1) have exactly the stated elevations.
Q4
Tier 1 · Easy

4

A vertical cylinder has radius 33 cm and height 88 cm. Write down the shape and dimensions of its plan.

(2)

(Total for Question 4 is 2 marks)

Mark scheme

Mark scheme for question 4
QuestionAnswerMarkMark scheme
4
  • A circle of diameter 66 cm
2Viewed from above, a vertical cylinder appears as its circular base. The diameter is twice the radius, so it is 2×3=62\times3=6 cm.
Q5
Tier 2 · Standard

5

A triangular prism is 77 cm long. Each end face is a right-angled triangle with a horizontal base 44 cm and a vertical side 33 cm on the left. Write down the shapes and dimensions of the plan and of the elevation seen when looking at an end face with the vertical side on the left.

(3)

(Total for Question 5 is 3 marks)

Mark scheme

Mark scheme for question 5
QuestionAnswerMarkMark scheme
5
  • Plan: a rectangle 77 cm by 44 cm; elevation: a right-angled triangle with horizontal base 44 cm and vertical left side 33 cm
3The plan shows the 77 cm length and 44 cm base, giving a 77 cm by 44 cm rectangle; the sloping face meets the top edge directly above the left-hand side of the base, so no extra line appears inside the rectangle. Looking at the end with the vertical side on the left shows the end face in true size, so the elevation is a right-angled triangle with a 44 cm horizontal base and a 33 cm vertical side on the left.
Q6
Tier 3 · Hard

6

A solid consists of a base cuboid 88 cm long, 55 cm deep and 22 cm high, with a second cuboid 33 cm long, 55 cm deep and 44 cm high. The second cuboid sits on top of the left-hand 33 cm of the base. Describe the plan, the front elevation viewed along the depth, and the side elevation viewed from the right.

(4)

(Total for Question 6 is 4 marks)

Mark scheme

Mark scheme for question 6
QuestionAnswerMarkMark scheme
6
  • Plan: an 88 cm by 55 cm rectangle with a line across the full depth 33 cm from the left end; front elevation: a step shape, 33 cm wide and 66 cm high on the left then 55 cm wide and 22 cm high; right side elevation: a 55 cm by 66 cm rectangle with a horizontal line 22 cm above its base.
4From above, both cuboids have the same depth, so the footprint is 88 cm by 55 cm and the top cuboid ends 33 cm from the left. From the front, the total height under the top cuboid is 2+4=62+4=6 cm for the first 33 cm, while the remaining width is 8−3=58-3=5 cm at height 22 cm. From the right, the maximum height along the length is 66 cm across the full 55 cm depth; the top of the base gives a horizontal line at height 22 cm.
Q7
Tier 2 · Standard

7

A right circular cone stands vertically with radius 44 cm and perpendicular height 99 cm. Write down the shapes and dimensions of its plan and its front elevation.

(3)

(Total for Question 7 is 3 marks)

Mark scheme

Mark scheme for question 7
QuestionAnswerMarkMark scheme
7
  • Plan: a circle of diameter 88 cm; front elevation: an isosceles triangle with base 88 cm and height 99 cm
3From above, the cone shows its circular base, whose diameter is 2×4=82\times4=8 cm. From the front, the circular base projects to an 88 cm line and the apex is 99 cm above its midpoint, giving an isosceles triangle of base 88 cm and height 99 cm.
Q8
Tier 3 · Hard

8

A right circular cylinder has radius 33 cm and length 1010 cm. Its axis is horizontal and runs from west to east. Write down the shapes and dimensions of the plan, the elevation viewed from the east, and the elevation viewed from the south.

(4)

(Total for Question 8 is 4 marks)

Mark scheme

Mark scheme for question 8
QuestionAnswerMarkMark scheme
8
  • Plan: a rectangle 1010 cm by 66 cm; east elevation: a circle of diameter 66 cm; south elevation: a rectangle 1010 cm by 66 cm
4The cylinder extends 1010 cm east-west and has diameter 2×3=62\times3=6 cm. From above, these are the plan's two dimensions, so the plan is a 1010 cm by 66 cm rectangle. Looking from the east is along the axis, so the elevation is the circular end of diameter 66 cm. Looking from the south shows the length and diameter, giving a 1010 cm by 66 cm rectangle.
Q9
Tier 3 · Hard

9

A pentagonal prism is 1010 cm long from west to east. Each end is shaped like a house: a horizontal base 66 cm wide, vertical walls 33 cm high and a roof apex centred 55 cm above the base. Describe the plan, the east elevation and the south elevation, including the ridge and eave lines.

(5)

(Total for Question 9 is 5 marks)

Mark scheme

Mark scheme for question 9
QuestionAnswerMarkMark scheme
9
  • Plan: a 1010 cm by 66 cm rectangle with the 1010 cm ridge line midway between its long sides; east elevation: the house-shaped pentagon, 66 cm wide with 33 cm walls and total height 55 cm; south elevation: a 1010 cm by 55 cm rectangle with a horizontal eave line 33 cm above the base
5From above, the prism occupies a 1010 cm by 66 cm rectangle and the roof ridge runs west-east along its centre. Looking from the east shows an end face: width 66 cm, vertical sides to height 33 cm and a centred apex at height 55 cm. Looking from the south shows the 1010 cm length and maximum 55 cm height; the wall-to-roof join gives a horizontal eave line at height 33 cm. End-face coordinates (0,0),(6,0),(6,3),(3,5),(0,3)(0,0),(6,0),(6,3),(3,5),(0,3) extruded 1010 cm verify one configuration.
Q10
Tier 3 · Hard

10

A cuboid is 1212 cm wide, 88 cm deep and 44 cm high. A square-based pyramid is fixed centrally on its top face. The pyramid has a 66 cm by 66 cm base and a perpendicular height of 55 cm. Describe the plan, front elevation and side elevation, including the projected apex, all visible joins and the total height.

(5)

(Total for Question 10 is 5 marks)

Mark scheme

Mark scheme for question 10
QuestionAnswerMarkMark scheme
10
  • Plan: a 1212 cm by 88 cm rectangle containing a centred 66 cm square, with the square's four corners joined to its centre; front elevation: a 1212 cm by 44 cm rectangle topped centrally by an isosceles triangle of base 66 cm and height 55 cm; side elevation: an 88 cm by 44 cm rectangle topped centrally by the same 66 cm by 55 cm triangle; total height =9=9 cm
5From above, the cuboid gives a 1212 cm by 88 cm rectangle. The centred pyramid base gives a 66 cm square, and its four sloping edges project from the base corners to the central apex. From the front, the cuboid is a 1212 cm by 44 cm rectangle and the pyramid is a centred isosceles triangle of base 66 cm and height 55 cm. From the side, the corresponding rectangle is 88 cm by 44 cm and the pyramid again projects as a 66 cm by 55 cm triangle. The total height is 4+5=94+5=9 cm. Coordinates with cuboid ranges −6≤x≤6-6\leq x\leq6, −4≤y≤4-4\leq y\leq4, 0≤z≤40\leq z\leq4, pyramid-base corners (±3,±3,4)(\pm3,\pm3,4) and apex (0,0,9)(0,0,9) verify one unique centred labelled configuration.

Verified exam appearances

SeriesPaperQuestionMarksCalculatorTierLinks
2022-112FQ192AllowedFoundationQPMS
2024-063HQ33AllowedHigherQPMS
2019-061FQ252Non-calculatorFoundationQPMS
2022-061FQ223Non-calculatorFoundationQPMS
2023-113FQ193AllowedFoundationQPMS
2024-063FQ243AllowedFoundationQPMS
2019-061HQ42Non-calculatorHigherQPMS
2022-112HQ22AllowedHigherQPMS

Other points in G Geometry and measures

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