Scale Drawing - Class 8 Mathematics Revision Notes

Scale Drawing

Worked Exercise

1. The distance between two villages is 6.4KM. On the map of the region this distance is represented by a line 1.6 cm long. What is the scale of the map?
   1. 1: 400000
   2. 1: 40000
   3. 1: 4000 
   4. 1: 4
      Working
      Actual distance = 6.4 km
      Drawing length = 1.6cm
      1 cm on the map = ^6.4/_1.6
      = 4km on the ground
      But 1 km = (1000 x 100) cm
      4km = 4 x 1000 x 100
      = 400000cm
      Therefore scale = 1: 400000
      The correct answer is A (1: 400000)
2. A rectangular field measures 105 m. On a scale drawing of the field, the longer side is 7cm.What is the measurement of the width on this scale drawing?
   1. 5 cm
   2. 50 cm
   3. 500 cm
   4. 7.35cm
      Working
      7 cm represents 105 m
      1 cm represents (105 ÷ 7)
      Scale used,
      1 cm represents 15m
             ?                  75m
      = ^{(75 x 1)}/₁₅
      5cm
      The correct answer is 5cm (A)
3. The scale on a plan is 1:20. How many cm will represent 1m on this plan?
   1. 50 cm
   2. 50 cm
   3. 5 cm
   4. 2 cm
      Working
      1 : 20 scale means 1 cm on a drawing represents 20 cm on the ground.
      1 cm represents 20cm
         ?                      100cm
      =¹⁰⁰/₂₀
      = 5cm
      The correct answer is C (5cm)
4. A rectangular field measuring 720m by 550m is to be represented on a scale drawing using the scale 1: 10,000. What is the perimeter of the drawing in centimetres?
   1. 0.254
   2. 2.54
   3. 25.4
   4. 254
      Working
      1: 10000 means 1 cm on the map represents 10000 cm on the ground
      If 1 cm = 10,0000cm
      ? = 72,000cm
      = (⁷²⁰⁰⁰/₁₀₀₀₀) cm
      = 7.2cm
      If 1cm = 10,000cm
      = 55,000cm
      = ( ^55,000/_10,000 ) cm
      = 5.5cm
      Perimeter
      
      P = 2(L+W)
      = 2 (7.2 + 5.5)
      = 25.4 cm
      The correct answer is (C)
5. The scale of a map is 1: 50000. What is the length of this map of a road 20km long?
   1. 40cm 
   2. 400 cm 
   3. 4000 cm
   4. 4 cm
      Working
      Scale 1 : 50000 means 1cm on the map represents 50000 cm on the ground.
      20 km = 20 x 1000 x 100
      = 2000000 cm
      50,000cm represents = 1 cm
      2,000,000 represents = 2,000,000 ÷ 50,000
      = 40cm
      The correct answer is A (40 cm)