Scale Drawings

Worked example

1. 1

   $\text{measure: }6\text{ cm}$ — Put the 0 of your ruler on one town and read where the other town is. This is the map distance.

2. 2

   $6\times 25=150\text{ km}$ — Drawing to real: multiply. Each of the 6 centimetres stands for 25 km, so 6 lots of 25 km.

Worked example

1. 1

   $\text{real: }36\text{ km},\text{scale }1\text{ cm to }8\text{ km}$ — The question. You need a length to draw, so you go from real life to the drawing.

2. 2

   $36÷8=4.5\text{ cm}$ — Real to drawing: divide. Count how many 8 km pieces fit into 36 km — each piece is 1 cm.

3. 3

   $\text{draw }4.5\text{ cm}$ — Put the 0 of your ruler on the start point and mark the point at 4.5 cm, along the bearing if one is given.

Worked example

1. 1

   $\text{put the }0\text{ on }A$ — The 0 mark is often a little way in from the end of the ruler, so line up the 0 with A, not the edge.

2. 2

   $\text{read at }B:5\text{ cm and }3\text{ mm}$ — Read the last whole centimetre, then count the small marks after it. Each small mark is 1 mm.

3. 3

   $AB=5.3\text{ cm}=53\text{ mm}$ — 3 mm is 0.3 cm, and 1 cm is 10 mm. Write the unit the question asks for — with no unit you can lose a mark.

Worked example

1. 1

   $90\text{ m}=9000\text{ cm}$ — 1 : 250 means 1 cm on the model is 250 cm on the ship, so work in centimetres. There are 100 cm in a metre: 90 × 100.

2. 2

   $9000÷250=36\text{ cm}$ — Real to model: divide. The model is 250 times smaller than the ship.

Worked example

1. 1

   $4.2\text{ cm},1:25000$ — The question. Real lengths are 25 000 times bigger than the map, in the same unit.

2. 2

   $4.2\times 25000=105000\text{ cm}$ — Map to real: multiply by n. The answer is in centimetres, because the map length was in centimetres.

3. 3

   $105000÷100=1050\text{ m}$ — There are 100 cm in a metre, so divide by 100 to get metres.

4. 4

   $1050÷1000=1.05\text{ km}$ — There are 1000 m in a kilometre, so divide by 1000. Now it is in km, as asked.

Worked example

1. 1

   $4\text{ cm}\to 100\text{ m}$ — The scale. 4 cm on the drawing stands for 100 m in real life.

2. 2

   $1\text{ cm}\to 100÷4=25\text{ m}$ — Divide both sides by 4, so you know what one centimetre stands for. Now it is an ordinary scale.

3. 3

   $\text{measure: }7.4\text{ cm}$ — Measure the path with the 0 of your ruler on its start.

4. 4

   $7.4\times 25=185\text{ m}$ — Drawing to real: multiply by what 1 cm stands for.

Worked example

1. 1

   $3\text{ km}=3000\text{ m}$ — Both parts of a ratio must be in the same unit. Start with km to m: there are 1000 m in a km.

2. 2

   $3000\text{ m}=300000\text{ cm}$ — Then m to cm: there are 100 cm in a metre. Now both lengths are in centimetres.

3. 3

   $6:300000$ — Write the ratio map : real, with no units, because they now match.

4. 4

   $1:50000$ — Divide both sides by 6 so the map side is 1. 300 000 ÷ 6 = 50 000.

Worked example

1. 1

   $8\text{ cm}\to 2400\text{ m}$ — Measure the drawing, and write the real distance from the question next to it.

2. 2

   $1\text{ cm}\to 2400÷8=300\text{ m}$ — Divide both by 8 to find what one centimetre stands for.

Worked example

1. 1

   $5\times 4=20\text{ m}$ — Change the length to real life: each cm is 4 m, so the real length is 20 m.

2. 2

   $3.5\times 4=14\text{ m}$ — Change the width the same way: the real width is 14 m.

3. 3

   $20\times 14=280{\text{ m}}^2$ — Now multiply real length by real width. Area units are squared: m².