Scale Drawing

12 Grade 8 Mathematics questions on Scale Drawing, with worked marking schemes. 12 questions are available on this topic in full.

1. Question 1

   1 mark

   A scale of 1:200 means 1 cm represents what actual length?

   A. 20 m

   B. 2 m

   C. 200 m

   D. 0.2 m

   (1 mark)

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2. Question 2

   1 mark

   A map has a scale of 1:25,000. What actual distance does 5 cm represent?

   A. 1.25 km

   B. 12.5 km

   C. 125 km

   D. 0.125 km

   (1 mark)

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3. Question 3

   3 marks

   A garden measures 45 m by 30 m. Using a scale of 1:500, find the dimensions of the garden on the plan.

   (3 marks)

   Marking scheme

   A scale of $1:500$ has no units, so both measurements must be in the same unit. Change the metres to centimetres: $45$ m $=4,500$ cm and $30$ m $=3,000$ cm. (1)

   Divide each by $500$ to get the plan length: $4,500÷500=9$ cm. (1)

   And the plan width: $3,000÷500=6$ cm. (1)

   Final answer: the plan is $9$ cm by $6$ cm.

4. Question 4

   1 mark

   A map has a scale of 1:50,000. How long is a 4 km road on the map?

   A. 2 cm

   B. 80 cm

   C. 8 cm

   D. 20 cm

   (1 mark)

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5. Question 5

   1 mark

   On a drawing, 1 cm represents 8 km. How is a river 56 km long drawn?

   A. 448 cm

   B. 7 cm

   C. 64 cm

   D. 48 cm

   (1 mark)

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6. Question 6

   1 mark

   A scale is 1:500. How is a wall 15 m long drawn on the plan?

   A. 30 cm

   B. 7500 cm

   C. 3 cm

   D. 0.3 cm

   (1 mark)

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7. Question 7

   1 mark

   A map has a scale of 1:20,000. What actual distance does 2.5 cm represent?

   A. 50 m

   B. 5000 m

   C. 250 m

   D. 500 m

   (1 mark)

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8. Question 8

   1 mark

   A plot is 60 m long. Using a scale of 1 cm to 10 m, what is its length on the drawing?

   A. 6 cm

   B. 600 cm

   C. 0.6 cm

   D. 60 cm

   (1 mark)

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9. Question 9

   1 mark

   A map has a scale of 1:100,000. What actual distance does 3 cm on the map represent?

   A. 3 km

   B. 30 km

   C. 300 km

   D. 0.3 km

   (1 mark)

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10. Question 10

    3 marks

    A rectangular field measures 80 m by 50 m. Using a scale of 1 cm to 10 m, find the dimensions of the field on the drawing.

    (3 marks)

    Marking scheme

    The scale $1$ cm to $10$ m means every $10$ m on the ground is drawn as $1$ cm, so divide each real measurement by $10$. (1)

    Length: $80÷10=8$ cm. (1)

    Width: $50÷10=5$ cm. (1)

    Final answer: the drawing is $8$ cm by $5$ cm.

11. Question 11

    1 mark

    On a drawing, 1 cm represents 5 m. How is a wall 35 m long drawn?

    A. 175 cm

    B. 7 cm

    C. 30 cm

    D. 40 cm

    (1 mark)

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12. Question 12

    3 marks

    A map has a scale of 1:50,000. The distance between two towns on the map is 6 cm. Find the actual distance between the towns in kilometres.

    (3 marks)

    Marking scheme

    A scale of $1:50,000$ means one unit on the map stands for $50,000$ of the same units on the ground, so multiply the map distance by $50,000$. (1)

    $6\times 50,000=300,000$ cm. (1)

    Convert to kilometres: $1$ km $=100,000$ cm, so $300,000÷100,000=3$. (1)

    Final answer: $3$ km.

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