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Measurement, plans and scale drawings

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Notes de leçon

Units and conversions

  • Length: 10 mm = 1 cm; 100 cm = 1 m; 1000 m = 1 km. Mass: 1000 g = 1 kg; 1000 kg = 1 tonne. Capacity: 1000 ml = 1 litre.
  • Compound units: speed (m/s, km/h), density (g/cm³), pressure. Convert 72 km/h to m/s: 72 \times \frac{1000}{3600} = 20 m/s.
  • Time: 60 s = 1 min; 60 min = 1 h. Convert decimal hours carefully: 2.5 h = 2 h 30 min.

Scale and maps

  • A scale 1 : 50 000 means 1 cm on the map is 50 000 cm = 500 m in real life.
  • Scale drawings: choose a scale, measure with a ruler and protractor, and convert lengths back.
  • A ratio scale has no units; a "1 cm to 5 m" scale needs conversion.
  • Area scales by the square of the length scale. At 1 : 20 000, 1 cm represents 200 m and 1 cm² represents 40 000 m².

Scale 1 : 50 000

Scale 1 : 50 0001 cm represents 0.5 kmMap (cm)Real (km)0010.52131.5424 cm on the map = 2 km in reality

Bearings

  • A bearing is an angle measured clockwise from north, written with three figures (e.g. 045°, 270°).
  • Add 180° and subtract 360° if the result is 360° or more. Thus 070° reverses to 250°, and 180° reverses to 000°.

Bearing of Q from P

Bearing of Q from PN070°12 kmPQ

Compound measures

  • Speed = distance ÷ time; density = mass ÷ volume; pressure = force ÷ area.
  • Use the formula triangle or rearrange: d = s \times t.

Constructions

  • Use a ruler, protractor and compasses: construct triangles (SSS, SAS, ASA), the perpendicular bisector of a line, the angle bisector, and a perpendicular from a point to a line. Leave construction arcs visible.

Plans and elevations

  • A plan is the view from above; front and side elevations show the corresponding vertical views.
  • For a 6 cm by 4 cm by 2 cm cuboid, the plan is 6 × 4 cm, front elevation 6 × 2 cm and side elevation 4 × 2 cm. Use a common scale.

Plan, front and side views

Plan, front and side viewsPlan6 cmVertical: 4 cmFront6 cmVertical: 2 cmSide4 cmVertical: 2 cmAll three views use the same scale.

Diapos

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Questions d'entraînement

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  1. 1.How many millimetres are in 1 cm?

    Easy
    • A10
    • B100
    • C1000
    • D1

  2. 2.How many metres are in 1 km?

    Easy
    • A10
    • B100
    • C1000
    • D10 000

  3. 3.Convert 3.5 km to metres.

    Easy
    • A350 m
    • B3500 m
    • C35 000 m
    • D0.35 m

  4. 4.Convert 2500 g to kg.

    Easy
    • A0.25 kg
    • B2.5 kg
    • C25 kg
    • D250 kg

  5. 5.What is 2.5 hours in hours and minutes?

    Easy
    • A2 h 5 min
    • B2 h 30 min
    • C2 h 50 min
    • D2 h 25 min

  6. 6.On a map with scale 1 : 50 000, 3 cm represents:

    Easy
    • A150 m
    • B1.5 km
    • C15 km
    • D150 km

  7. 7.A scale is 1 cm to 5 m. A room is 40 m long. How long is the drawing?

    Easy
    • A8 cm
    • B20 cm
    • C200 cm
    • D0.8 cm

  8. 8.What is the bearing of east?

    Easy
    • A000°
    • B090°
    • C180°
    • D270°

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