◄UNIT 11: Drawing and construction of anglesUNIT 13:Calculating the circumference of a circle and the volume of cuboids and cubes►

UNIT 12:Interpreting and constructing scale drawings

  • UNIT 12:Interpreting and constructing scale drawings

    12.1 Concept of scale drawing
    Activity 12.1
    Draw diagrams to represent the following in your books.
    (a) Your classroom.
    (b) The distance between your classroom and the office.
    (c) The chalkboard.
    Measure and record actual distances of real objects you have drawn.
    Measure the lengths of your drawings.
    Compare the actual measurements with their drawing measurements.

    Which distances are bigger? Make a presentation to the class.

    Activity 12.2
    • Measure the length of the top of the desk drawn below. Record its

    length in cm.

    s

    • Now measure the length of your actual desk in cm.

    • Compare the drawing length with the actual length.

    Tip: Actual distances may not be possible to fit in a drawing on a paper.
    We draw them to the size of the paper using a shorter distances.
    When we do that, we have drawn objects to a scale. For example, a
    distance of 12 km road can be drawn as 12 cm on paper. This way,

    we have drawn to scale.

    Practice Activity 12.1
    Study the following:
    (a) What are their actual lengths?
    (b) Measure their drawing lengths.

    (c) Explain why a diagram of a large object can fit on paper.

    m

    12.2 Finding scale
    Activity 12.3
    • Cover the top of your desk with sheets of paper. How many sheets

    of paper have you used?

    s

    • Measure the actual width and length of your desk. Record them.
    • Try to draw the top of your desk to cover 1 page paper. What are the
    width and length of your drawing? What scale have you used?
    • Make presentations to the class.

    Tip    : To find a scale;
    (i) Measure drawing length
    (ii) Measure the actual length of the object in the same unit as the

    drawing length.

    (iii) Scale = Drawing length

                       Actual length = Drawing length : Actual length

    Example 12.1
    (a) 12 sheets of paper fit on top of a desk. The top of a desk is drawn on
    one piece of paper. Find the scale.

    Solution

    • 12 sheets covering top of desk.

    j

    • To draw one sheet, I divide actual lengths by 12.
    The scale is 1:12
    (b) The actual length of a path is 20 m. It is drawn using a line 5 cm

    long. What scale has been used?

    9

    Practice Activity 12.2
    1. The actual lengths for various items were measured. Their drawing

    lengths were recorded as follows.

    d

    Calculate the scale used and fill in the table above accordingly.
    2. The actual distance for a section of road is 25 km. It is drawn on a map
    using a 5 cm line. Explain how to find the scale of the map.
    3. A flag post is drawn to scale. Its drawing height is 5 cm. Suppose the
    actual height is 10 m. Find the scale used to draw the flag post.
    4. The actual length of the Nyabarongo River is 300 km. On a map, it is
    represented by a 30 cm long line. Discuss how to find the scale used of
    the map.
    5. The actual perimeter of a rectangular plot is 100 m. The plot was

    drawn to scale as shown below.

    f

    (a) Explain how to find the length and width of the plot in the drawing.
    (b) Explain how to find the perimeter of the scale drawing.

    (c) Explain the scale used in drawing the plot.

    12.3 Constructing scale drawings
    Activity 12.4
    • Measure the actual length of your classroom. Use a scale to draw a
    line to represent the length of your classroom.
    • Measure the width and length of your classroom. Use a scale to draw
    the shape of the floor.
    • What is the actual distance from
    (i) your classroom to assembly?
    (ii) your classroom to the office?
    Draw a simple map showing distances for:
    Classroom point to office point and assembly point. Use a suitable scale.

    Tip:     To make a scale drawing
    (i) Know the actual distances
    (ii) Choose a good scale
    (iii) Find drawing distances

    (iv) Draw the diagram

    Example 12.2

    Look at the sketch of a section of a road.

    b

    Explain how you would use a scale of 1:500 to show the road on paper.
    Solution
    1 cm represents 500 cm or 5 m. From 50 m, the drawing length is
    50/5 = 10 cm. From 5 m, we have a drawing width of 5/5= 1 cm.
    x

    Example 12.3
    A dining hall measures 40 m long and 35 m wide. Using a scale 1:1 000,

    explain how to make a scale drawing of the hall.

    Solution

    c

    Practice Activity 12.3
    1. Using a scale of 1:100, make a scale drawing of the following.
    (a) A rectangle measuring 7 m by 3 m.
    (b) An equilateral triangle with 5 m sides.
    (c) A square with 4 m sides.
    2. Using a scale of 1:500 000, draw lines to represent the following
    distances.
    (a) 15 km      (b) 26.5 km      (c) 45 km      (d) 10 km
    3. Using a scale 1:1 000, describe how to draw lines to represent the
    following length. Present to the class.
    (a) 7 200 cm    (b) 8 000 cm        (c) 6 800 cm
    4. (a) Measure the actual distances of the following:
    (i) Length and height of chalkboard.
    (ii) Length and width of playground.

    (b) Discuss how to draw them to scale.

    5. Look at the sketch below. The actual distances are stated

    f

    Draw the diagram to a scale 1:400.
    (a) What is the drawing length from A to B?
    (b) What is the drawing distance AE?

    (c) Explain your answers in (a) and (b).

    12.4 Finding actual distance
    Activity 12.5

    • Measure the length of the line below. It represents a ruler.

    f

    The scale used is 1:10
    Find the actual length of the ruler.
    • Consider 15 cm ruler, 30 cm ruler and a metre-rule. Which of them

    has its length represented by AB? Discuss your answer.

    Example 12.4

    In a map, a section of road is represented by the line below.

    d

    The scale used is 1:10 000
    (a) Measure line AB, BC. What distance is AC through B?
    (b) Interpret the scale.
    (c) Find the actual distance AB and AC. Find the actual distance of the
    section of the road.
    Solution
    (a) Drawing lengths: AB = 7 cm, BC = 5 cm.
    AC through B = (7 + 5) cm = 12 cm.
    (b) The scale 1:10 000 means; 1 cm drawing length represents 10 000 cm
    or 100 m actual distance on the road.
    (c) Actual distance;
    AB = 7 × 100 m = 700 m
    BC = 5 × 100 m = 500 m

    Distance of the road = 700 m + 500 m = 1 200 m or 1.2 km

    Tip:
    To find actual distance
    (i) Measure drawing length.                 (ii) Interpret the scale.
    (iii) Use formula, Actual distance = drawing length × value of scale

    (represented by 1 cm).

    Practice Activity 12.4
    1. The drawing length for a section of a river is 10 cm. The scale used was
    1:2 500. Find the actual length of the section of the river (in m).
    2. Below is a section of road joining towns W, X, Y, Z. Measure the
    drawing lengths and fill in the table accordingly. The scale used was

    1: 100 000. Calculate the actual distances.

    v

    d

    3. Given the scale 1:200 000, explain how to find the actual lengths of the
    following.
    (a) 5 cm     (b) 2.5 cm      (c) 3.2 cm       (d) 8 cm

    4. Below is a scale drawing of a floor of classrooms.

    s

    Scale used is 1:40 000
    Explain how to find the actual distances in metres for the following
    distances.
    (i) AB          (ii) BC              (iii) CD            (iv) DE

    (v) AH         (vi) FE             (vii) AD            (viii) GE

    12.5 Finding the drawing length

    Activity 12.6
    • Measure the actual distance from your classroom to the assembly
    grounds. Use a metre rule or tape measure.
    • Measure the actual lengths of your classroom. Record your results
    in the table below.

    • Use a scale 1:1 000 to find drawing lengths for each object.

    b

    Present your findings.

    Example 12.5
    The sketch below shows actual distances between towns P, Q, R and S.

    It is to be represented in a scale drawing. The scale to use is 1:200 000.

    h

    (a) Interpret the scale.
    (b) Explain how to get the drawing measurements between the towns.
    (i) PQ                     (ii) QR                (iii) RS
    (c) Make a scale drawing of the distances between towns.
    Solution
    (a) The scale 1:200 000 means 1 cm represents 200 000 cm or 2 km.
    Thus, 1 cm on the drawing represents 2 km of actual distance.
    (b) (i) 1 cm represents 2 km. So PQ = 12 km.
    12 km is represented by (12/2 ) cm = 6 cm.
    (ii) Actual distance QR = 18 km.
    Drawing length for QR = (18/2 ) cm = 9 cm.
    (iii) Actual distance RS = 10 km.
    Drawing length for RS is (10/2 ) cm = 5 cm
    z


    Practice Activity 12.5
    1. Use the scale 1:10 000. Find the drawing lengths for these:
    (a) A section of river that is 350 m
    (b) A section of road that is 820 m
    (c) The length of school path that is 225 m
    2. Use the scale 1: 100 000. Find the drawing length for each of the
    following:
    (a) A road joining towns PQ = 60 km
    (b) A railway line joining towns XY = 225 km
    (c) A length of river joining two provinces = 200 km.
    3. The distance between two towns is 120 km. Use a scale of 1:300 000.
    Find the drawing length for the two towns.
    4. Using the scale of 1:2 000, make the following scale drawings. Then
    explain your work.
    (a) Rectangular field measuring 80 m by 60 m.
    (b) A path which is 240 m long.
    5. Using the scale of 1:30 000, make scale drawings of the following. Then
    discuss your work.
    (a) A square field with sides of 1 200 m.
    (b) A section of a road which is 2 700 m.
    6. A road between two towns is 56 km long. It is represented in a map
    with a scale of 1:1 000 000. What is the drawing length of the road in

    the map? Justify your answer.

    Revision Activity 12

    1. A section of river is 1 720 m. It is drawn on a map. The drawing
    length is 17.2 cm. Find the scale used in the map.
    2. A building measures 24 m by 10 m. It is to be drawn to scale on a
    paper measuring 30 cm by 20 cm. Discuss the appropriate scale to
    be used.
    3. Choose appropriate scales to be used to draw the following lengths?
    (a) 820 cm                   (b) 60 m                                  (c) 40 km
    4. What scale was used to make the following drawings? Measure the

    drawing lengths. The actual measurements are given.

    m

    Actual distances:
    PQ = 60 m

    QS = 30 m

    m

    5. In a scale drawing, a scale of 1:20 000 was used. Find the drawing
    length for a section of road that is 840 m.
    6. The diagram below is drawn to scale. It shows the roads joining

    various towns.

    m

    The actual distances are as follows:

    u

    (a) Explain how to find the drawing lengths between;
    (i) PQ                        (ii) QR                         (iii) RS
    (iv) ST                       (v) TU                         (vi) UV
    (b) Find the actual distance between Q and S through R.
    (c) Explain how to find the scale used for the map.

    7. The figure below has been drawn to scale at 1:500.

    g

    (a) Measure its length.                  (b) Measure its width.
    (c) Interpret the scale.                   (d) Find the actual length.
    (e) Find the actual width.              (f) Discuss your answer.
    8. Using the scale 1:1 000, make scale drawings of the following and
    discuss your answers.
    (a) Rectangle measuring 40 m by 20 m.
    (b) Square field whose sides are 50 m.
    (c) A rectangular field measuring 80 m by 60 m.
    9. In a map, a scale of 1:300 000 is used. Discuss the steps to follow to
    calculate the drawing length for these distances:

    (a) 21 km          (b) 27 km          (c) 36 km            (d) 15 km

    Word list
    Scale                       Actual length         Drawing length
    Scale drawing          Actual distance
    Task
    Do the following.
    (i) Read each word aloud to your friend.
    (ii) Write the meaning of each of the words above. Discuss with your friend.

    (iii) Write sentences using each of the words above. Read with your friend.

    ◄UNIT 11: Drawing and construction of anglesUNIT 13:Calculating the circumference of a circle and the volume of cuboids and cubes►