Plans and Elevations - Worksheets, Questions and Revision

18 original exam-style questions - 17 pages of questions with a full mark scheme - free printable PDF.

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GCSE · Geometry and Measures

4.17 Plans and Elevations

EDEXCEL 1MA1 · Calculator allowed · about 75 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
A 3D solid is viewed in three different ways, labelled A, B and C.
A: looking straight down at the solid from directly above.
B: looking horizontally at the solid from the front.
C: looking horizontally at the solid from one side.
(a)Write down the letter, A, B or C, that gives the plan of the solid.(1)
(b)Write down the letter, A, B or C, that gives the front elevation of the solid.(1)
(c)Write down the letter, A, B or C, that gives the side elevation of the solid.(1)
(Total for Question 1 is 3 marks)
2
A cuboid has length 6 cm, width 4 cm and height 3 cm. It stands on a table. Arrow F points towards the front face of the cuboid.
F 6 cm 3 cm 4 cm
(a)Write down the dimensions of the front elevation of the cuboid.(1)
(b)Write down the dimensions of the plan of the cuboid.(1)
(Total for Question 2 is 2 marks)
3
A solid cube has edges of length 5 cm. State whether each statement is True or False.
5 cm 5 cm 5 cm 5 cm 5 cm 5 cm 5 cm 5 cm 5 cm 5 cm 5 cm 5 cm
(a)The front elevation of the cube is a square measuring 5 cm by 5 cm.(1)
(b)The plan of the cube is a rectangle that is not a square.(1)
(c)The front elevation and the side elevation of the cube are exactly the same shape and size as each other.(1)
(Total for Question 3 is 3 marks)
4
The diagram shows a solid made from four identical 1 cm cubes joined edge-to-edge in a single straight row. Draw the front elevation of the solid, as viewed from arrow F, and state its dimensions.
4 cm 1 cm 1 cm F
(Total for Question 4 is 2 marks)
5
The diagram shows a solid built from 1 cm cubes standing on a grid. The numbers show how many cubes are stacked at each position.
Col 1 Col 2 Col 3 1 1 1 1 1 2 Row 1 (back) Row 2 (front) S F
(a)Draw the front elevation of the solid, as viewed from arrow F.(2)
(b)Draw the side elevation of the solid, as viewed from arrow S.(2)
(Total for Question 5 is 4 marks)
6
The diagram shows a flat solid made from three 1 cm cubes on a 2 by 2 grid (one grid position is empty).
1 1 1 0 Row 1 (back) Row 2 (front) Col 1 Col 2 F Numbers show height (in 1 cm cubes) at each position. 0 = no cube. Arrow F shows the front-view direction.
(a)Which of these is the correct plan of the solid?(1)
  • A) a 2 by 2 square
  • B) an L-shape made of 3 unit squares (the Row 2, Column 2 square is missing)
  • C) a 1 by 3 rectangle
  • D) a T-shape made of 4 unit squares
(b)Even though the plan is an L-shape, the front elevation of this solid is a plain 2 cm by 1 cm rectangle, with no gap visible. Give a reason why.(1)
(Total for Question 6 is 2 marks)
7
The diagram shows a solid made from 2 cm cubes standing on a grid. The numbers show how many cubes are stacked at each position.
Diagram NOT accurately drawn
Row 1 Row 2 3 1 2 2 1 1 Numbers = height of stack (in 2 cm cubes)
(a)How many 2 cm cubes are used to build the solid?(1)
(b)Work out the total volume of the solid.(2)
(Total for Question 7 is 3 marks)
8
A garden shed has a rectangular floor plan measuring 3 m by 2 m, but a 1 m by 1 m square has been removed from one corner to make room for a water butt, forming an L-shaped plan. All corners are right angles.
Diagram NOT accurately drawn
water butt 2 m 1 m 1 m 1 m 3 m 2 m
(a)Work out the area of the shed's floor plan.(2)
(b)Work out the perimeter of the shed's floor plan.(1)
(Total for Question 8 is 3 marks)
9
A cuboid has front elevation measuring 5 cm by 3 cm, side elevation measuring 2 cm by 3 cm, and plan measuring 5 cm by 2 cm.
Diagram NOT accurately drawn
Front elevation Side elevation Plan 5 cm 3 cm 2 cm 3 cm 5 cm 2 cm
(a)Write down the length, width and height of the cuboid.(1)
(b)Work out the volume of the cuboid.(2)
(Total for Question 9 is 3 marks)
10
A staircase-shaped solid is built from 1 cm cubes. Three vertical stacks of cubes stand in a single row, one directly behind the next, each stack 1 cube wide. The back stack is 3 cubes high, the middle stack is 2 cubes high, and the front stack is 1 cube high.
(a)Draw the plan of the solid.(1)
(b)Draw the side elevation of the solid, viewed from the side so the steps can be seen.(2)
(Total for Question 10 is 3 marks)
11
The diagram shows a solid built from 1 cm cubes standing on a 3 by 3 grid. The numbers show how many cubes are stacked at each position.
1 2 1 2 3 2 1 2 1 (Col1) (Col2) (Col3) F S
(a)Draw the front elevation of the solid.(2)
(b)Draw the side elevation of the solid.(2)
(Total for Question 11 is 4 marks)
12
A solid is built from 1 cm cubes. It is 4 cubes long and 2 cubes deep. In every column of cubes, the height is the same in the back row as it is in the front row. Four diagrams show possible front elevations, each 4 squares wide. The numbers show the height, in unit squares, of each column, left to right.
A) 1, 1, 2, 2
B) 2, 2, 1, 1
C) 2, 1, 1, 2
D) 1, 2, 2, 1
The solid's two tallest columns (height 2) are on the left, and its two shortest columns (height 1) are on the right.
(a)Which diagram, A, B, C or D, is the correct front elevation of the solid?(1)
  • A) 1, 1, 2, 2
  • B) 2, 2, 1, 1
  • C) 2, 1, 1, 2
  • D) 1, 2, 2, 1
(b)How many unit cubes make up the whole solid?(1)
(Total for Question 12 is 2 marks)
13
A cereal box is a cuboid. Standing upright in its usual position, the front elevation measures 8 cm by 24 cm, and the plan measures 8 cm by 5 cm. The box is then laid down so that the face which used to be the front elevation (8 cm by 24 cm) becomes the new plan view.
(a)Write down the dimensions of the new plan view.(1)
(b)Work out the height of the box in this new position.(1)
(c)Write down the dimensions of the two new elevations (the front and side elevations), giving each one's dimensions.(2)
(Total for Question 13 is 4 marks)
14
The plan of a solid, drawn on a centimetre grid, is an L-shape made from 5 unit squares, as shown. Every position in the plan has a stack of cubes exactly 3 cubes tall.
Diagram NOT accurately drawn
Plan (top view) Row 1 Row 2 X X . X X X 1 cm
(a)How many unit squares make up the plan?(1)
(b)Work out the total number of cubes in the solid.(2)
(Total for Question 14 is 3 marks)
15
A block of cheese is a cuboid 12 cm long, 6 cm high and 5 cm deep. A rectangular notch, 4 cm wide and 2 cm high, has been cut away from the top of the front face. The notch runs the full depth of the cheese and does not touch either end of the block.
Work out the area of the front elevation of the cheese (the shape you would see looking directly at the front face, including the notch).
Diagram NOT accurately drawn
12 cm 6 cm 5 cm 4 cm 2 cm
(Total for Question 15 is 4 marks)
16
The front elevation of a garden summerhouse is a rectangle with an isosceles triangle roof on top. The rectangle is 3.2 m wide and 2.1 m high. The triangular roof has a base of 3.2 m and a height of 0.9 m.
Work out the total area of the front elevation.
Diagram NOT accurately drawn
3.2 m 2.1 m 0.9 m
(Total for Question 16 is 4 marks)
17
The front elevation (cross-section) of a skateboard ramp is a trapezium. The two parallel sides are 0.4 m and 1.6 m, and the perpendicular distance between them is 0.8 m. The ramp is a prism, 2.5 m wide (front to back).
Diagram NOT accurately drawn
0.4 m 1.6 m 0.8 m 2.5 m
(a)Work out the area of the front elevation.(2)
(b)Work out the volume of the ramp.(2)
(Total for Question 17 is 4 marks)
18
The front elevation of a step-shaped prism is an L-shape, with these measurements: overall width 10 cm, overall height 8 cm, the height of the lower step (across the full width) is 3 cm, the width of the upper part is 4 cm, and the upper part rises a further 5 cm above the lower step. The prism is 6 cm deep (front to back).
Diagram NOT accurately drawn
10 cm 8 cm 3 cm 5 cm 4 cm 6 cm
(a)Work out the area of the front elevation.(2)
(b)Work out the perimeter of the front elevation.(2)
(c)The prism is 6 cm deep. Work out the total surface area of the solid.(3)
(Total for Question 18 is 7 marks)
Mark scheme · 4.17 Plans and Elevations

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18