Teach Me Maths

Scale Drawings and Maps

Question 11 mark

Priya measures the distance from her house to the beach on a map. It is 6 cm.

The scale of the map is 1 cm represents 5 km.

How far is it from Priya's house to the beach in real life? Give your answer in km.

Hint

Each centimetre on the map stands for 5 km in real life.

Worked solution

Priya measures the distance from her house to the beach on a map. It is 6 cm.

The scale of the map is 1 cm represents 5 km.

How far is it from Priya's house to the beach in real life? Give your answer in km.

  1. Each centimetre on the map is 5 km in real life, so multiply by 5.
  2. 6\times5=30, so the real distance is 30 km.

Question 21 mark

A cycle path is 21 km long.

Leo draws the path on a map. He uses a scale of 1 cm to 3 km.

How long is the path on Leo's map? Give your answer in cm.

Hint

Work out how many lots of 3 km there are in 21 km.

Worked solution

A cycle path is 21 km long.

Leo draws the path on a map. He uses a scale of 1 cm to 3 km.

How long is the path on Leo's map? Give your answer in cm.

  1. Each 3 km is drawn as 1 cm, so divide by 3.
  2. 21\div3=7, so the path is 7 cm long on the map.

Question 32 marks

A model of a car is made using a scale of 1:20

The model is 18 cm long.

Work out the length of the real car. Give your answer in centimetres.

Hint

A scale of 1:20 means the real car is 20 times as long as the model.

Worked solution

A model of a car is made using a scale of 1:20

The model is 18 cm long.

Work out the length of the real car. Give your answer in centimetres.

  1. Real length =18\times20.
  2. 18\times20=360, so the real car is 360 cm long.

Question 42 marks

A plan of a room is drawn using a scale of 1:50

On the plan, the length of the room is 8 cm.

Work out the real length of the room. Give your answer in metres.

Hint

Find the real length in centimetres first, then change it into metres.

Worked solution

A plan of a room is drawn using a scale of 1:50

On the plan, the length of the room is 8 cm.

Work out the real length of the room. Give your answer in metres.

  1. Real length =8\times50=400 cm.
  2. There are 100 cm in 1 m, so 400\div100=4 m.

Question 52 marks

The diagram shows a scale drawing of a rectangular garden on a square grid.

Each square on the grid represents 2 m.

Work out the real length of the longer side of the garden, in metres.

Hint

Count the squares along the longer side, then use the scale.

Worked solution

The diagram shows a scale drawing of a rectangular garden on a square grid.

Each square on the grid represents 2 m.

Work out the real length of the longer side of the garden, in metres.

  1. The longer side is 6 squares long.
  2. 6\times2=12, so the real length is 12 m.

Question 62 marks

Tom is planning a walk along a footpath. On his map, the footpath is 9 cm long.

The scale of the map is 1:50\,000

How long is the footpath in real life? Give your answer in kilometres.

Hint

Each 1 cm on the map is 50\,000 cm in real life. There are 100\,000 cm in 1 km.

Worked solution

Tom is planning a walk along a footpath. On his map, the footpath is 9 cm long.

The scale of the map is 1:50\,000

How long is the footpath in real life? Give your answer in kilometres.

  1. Real length =9\times50\,000=450\,000 cm.
  2. 450\,000\div100=4500 m, and 4500\div1000=4.5 km.

Question 72 marks

Two villages are 6 km apart.

Sara marks the two villages on her map. The scale of her map is 1:40\,000

How far apart are the villages on Sara's map? Give your answer in centimetres.

Hint

Change 6 km into centimetres first.

Worked solution

Two villages are 6 km apart.

Sara marks the two villages on her map. The scale of her map is 1:40\,000

How far apart are the villages on Sara's map? Give your answer in centimetres.

  1. 6 km =6000 m =600\,000 cm.
  2. Map distance =600\,000\div40\,000=15 cm.

Question 81 mark

On a plan, 1 cm represents 2 m.

The scale of the plan can be written as the ratio 1:n

Work out the value of n.

Hint

Write 2 m in centimetres, so both parts of the ratio are in the same units.

Worked solution

On a plan, 1 cm represents 2 m.

The scale of the plan can be written as the ratio 1:n

Work out the value of n.

  1. 2 m =200 cm.
  2. So 1 cm represents 200 cm, and the scale is 1:200. The value of n is 200.

Question 92 marks

A bus goes from the station to the library, then from the library to the park.

On a map, the station to the library is 4.5 cm. The library to the park is 3.5 cm.

The map has a scale of 1 cm to 2 km.

Work out the real distance the bus travels from the station to the park. Give your answer in km.

Hint

Add the two map lengths first, then use the scale.

Worked solution

A bus goes from the station to the library, then from the library to the park.

On a map, the station to the library is 4.5 cm. The library to the park is 3.5 cm.

The map has a scale of 1 cm to 2 km.

Work out the real distance the bus travels from the station to the park. Give your answer in km.

  1. Total map length =4.5+3.5=8 cm.
  2. Real distance =8\times2=16 km.

Question 102 marks

On a map, a length of 5 cm represents a real distance of 35 km.

The scale of the map is 1 cm represents k km.

Work out the value of k.

Hint

Find the real distance shown by just 1 cm of the map.

Worked solution

On a map, a length of 5 cm represents a real distance of 35 km.

The scale of the map is 1 cm represents k km.

Work out the value of k.

  1. 5 cm represents 35 km.
  2. So 1 cm represents 35\div5=7 km, and k=7.

Question 113 marks

The diagram shows a scale drawing of a rectangular playground on a square grid.

Each square on the grid represents 3 m.

Work out the real perimeter of the playground. Give your answer in metres.

Hint

Find the real length and the real width first, then add all four sides.

Worked solution

The diagram shows a scale drawing of a rectangular playground on a square grid.

Each square on the grid represents 3 m.

Work out the real perimeter of the playground. Give your answer in metres.

  1. The playground is 5 squares long and 3 squares wide.
  2. Real length =5\times3=15 m. Real width =3\times3=9 m.
  3. Perimeter =15+9+15+9=48 m.

Question 123 marks

A rectangular classroom is 9 m long and 6 m wide.

Ali makes a scale drawing of the classroom. He uses a scale of 1:200

(a)

Work out the length of the classroom on Ali's drawing. Give your answer in centimetres.

2 marks

(b)

Work out the width of the classroom on Ali's drawing. Give your answer in centimetres.

1 mark

Hint

Change the real lengths into centimetres, then divide by 200.

Worked solution

A rectangular classroom is 9 m long and 6 m wide.

Ali makes a scale drawing of the classroom. He uses a scale of 1:200

Part (a)

Work out the length of the classroom on Ali's drawing. Give your answer in centimetres.

  1. 9 m =900 cm.
  2. Length on the drawing =900\div200=4.5 cm.

Part (b)

Work out the width of the classroom on Ali's drawing. Give your answer in centimetres.

  1. 6 m =600 cm.
  2. Width on the drawing =600\div200=3 cm.

Question 132 marks

Jo has a scale drawing of a sailing boat.

On the drawing, the boat is 8 cm long and the mast is 5 cm tall.

The real boat is 12 m long.

Work out the real height of the mast. Give your answer in metres.

Hint

Use the length of the boat to find what 1 cm on the drawing represents.

Worked solution

Jo has a scale drawing of a sailing boat.

On the drawing, the boat is 8 cm long and the mast is 5 cm tall.

The real boat is 12 m long.

Work out the real height of the mast. Give your answer in metres.

  1. 8 cm represents 12 m, so 1 cm represents 12\div8=1.5 m.
  2. Real height of the mast =5\times1.5=7.5 m.

Question 143 marks

The diagram shows two routes from A to D on a map. The lengths shown are lengths on the map.

The scale of the map is 1 cm represents 5 km.

(a)

Which route is shorter?

1 mark

(b)

How much shorter is it in real life? Give your answer in km.

2 marks

Hint

Add the map lengths along each route.

Worked solution

The diagram shows two routes from A to D on a map. The lengths shown are lengths on the map.

The scale of the map is 1 cm represents 5 km.

Part (a)

Which route is shorter?

  1. The route through B
  2. The route through C
  3. They are the same length
  1. Through B: 3.2+4.5=7.7 cm on the map.
  2. Through C: 2.6+5.4=8 cm on the map.
  3. The route through B is shorter.

Part (b)

How much shorter is it in real life? Give your answer in km.

  1. Difference on the map =8-7.7=0.3 cm.
  2. Real difference =0.3\times5=1.5 km.

Question 153 marks

A cycle route has three sections.

On a map with a scale of 1 cm represents 3 km, the first section is 6 cm long and the second section is 3.5 cm long.

The whole route is 42 km long in real life.

Work out the length of the third section on the map. Give your answer in centimetres.

Hint

Work out the length of the whole route on the map first.

Worked solution

A cycle route has three sections.

On a map with a scale of 1 cm represents 3 km, the first section is 6 cm long and the second section is 3.5 cm long.

The whole route is 42 km long in real life.

Work out the length of the third section on the map. Give your answer in centimetres.

  1. Whole route on the map =42\div3=14 cm.
  2. First two sections =6+3.5=9.5 cm.
  3. Third section =14-9.5=4.5 cm.

Question 16Challenge4 marks

On a map with a scale of 1:250\,000, the distance between two towns is 12 cm.

Mia drives from one town to the other at an average speed of 40 km/h.

How many minutes does her journey take?

Hint

Find the real distance in km, then use time = distance ÷ speed.

Worked solution

On a map with a scale of 1:250\,000, the distance between two towns is 12 cm.

Mia drives from one town to the other at an average speed of 40 km/h.

How many minutes does her journey take?

  1. Real distance =12\times250\,000=3\,000\,000 cm.
  2. 3\,000\,000 cm =30\,000 m =30 km.
  3. Time =30\div40=0.75 hours.
  4. 0.75\times60=45 minutes.

Question 17Challenge3 marks

A plan of a patio is drawn to a scale of 1:50

On the plan, the patio is a rectangle 7 cm long and 6 cm wide.

Work out the real area of the patio. Give your answer in m².

Hint

Find the real length and width in metres before you work out the area.

Worked solution

A plan of a patio is drawn to a scale of 1:50

On the plan, the patio is a rectangle 7 cm long and 6 cm wide.

Work out the real area of the patio. Give your answer in m².

  1. Real length =7\times50=350 cm =3.5 m.
  2. Real width =6\times50=300 cm =3 m.
  3. Real area =3.5\times3=10.5 m².

Question 18Challenge3 marks

Leah has a plan of her bedroom drawn to a scale of 1:40

On the plan, there is a gap of 4.2 cm between the wall and the door.

Leah wants to put a wardrobe in this gap. The wardrobe is 175 cm wide.

(a)

Work out the real width of the gap. Give your answer in metres.

2 marks

(b)

Will the wardrobe fit in the gap?

1 mark

Hint

Each 1 cm on the plan is 40 cm in real life. Then change centimetres into metres.

Worked solution

Leah has a plan of her bedroom drawn to a scale of 1:40

On the plan, there is a gap of 4.2 cm between the wall and the door.

Leah wants to put a wardrobe in this gap. The wardrobe is 175 cm wide.

Part (a)

Work out the real width of the gap. Give your answer in metres.

  1. Real width =4.2\times40=168 cm.
  2. 168 cm =168\div100=1.68 m.

Part (b)

Will the wardrobe fit in the gap?

  1. Yes, it will fit
  2. No, it will not fit
  1. The gap is 1.68 m =168 cm wide, but the wardrobe is 175 cm wide.
  2. 175 is more than 168, so the wardrobe will not fit.

Question 19Challenge3 marks

A lake is 12 cm long on map A. Map A has a scale of 1:50\,000

Map B has a scale of 1 cm represents 4 km.

How long is the lake on map B? Give your answer in centimetres.

Hint

Use map A to find the real length of the lake in km first.

Worked solution

A lake is 12 cm long on map A. Map A has a scale of 1:50\,000

Map B has a scale of 1 cm represents 4 km.

How long is the lake on map B? Give your answer in centimetres.

  1. Real length =12\times50\,000=600\,000 cm.
  2. 600\,000 cm =6000 m =6 km.
  3. On map B: 6\div4=1.5 cm.

Question 20Challenge4 marks

Kate is planning a walk that starts and ends at A. She uses a map with a scale of 1:25\,000

Route 1 goes from A to B (14 cm on the map), B to C (16 cm) and C back to A (12 cm).

Route 2 goes from A to B (14 cm on the map), B to D (10 cm) and D back to A (13 cm).

Kate wants to walk no more than 10 km.

(a)

Work out the real length of Route 1. Give your answer in km.

3 marks

(b)

Which route or routes can Kate take?

1 mark

Hint

Add the map lengths for each route, then change them into real distances in km.

Worked solution

Kate is planning a walk that starts and ends at A. She uses a map with a scale of 1:25\,000

Route 1 goes from A to B (14 cm on the map), B to C (16 cm) and C back to A (12 cm).

Route 2 goes from A to B (14 cm on the map), B to D (10 cm) and D back to A (13 cm).

Kate wants to walk no more than 10 km.

Part (a)

Work out the real length of Route 1. Give your answer in km.

  1. Route 1 on the map =14+16+12=42 cm.
  2. Real length =42\times25\,000=1\,050\,000 cm.
  3. 1\,050\,000 cm =10\,500 m =10.5 km.

Part (b)

Which route or routes can Kate take?

  1. Route 1 only
  2. Route 2 only
  3. Both routes
  4. Neither route
  1. Route 2 on the map =14+10+13=37 cm.
  2. Real length =37\times25\,000=925\,000 cm =9.25 km.
  3. Route 1 is 10.5 km, which is more than 10 km. Route 2 is 9.25 km, which is less than 10 km.
  4. Kate can take Route 2 only.

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