Scale Drawings and Models Quiz

Grade 7 · Math · Quiz

Test your ability to apply scale factors and proportions to real-world drawing and model problems.

Questions

  1. A blueprint scale is 1 inch = 8 feet. A room measures 3.5 inches on the blueprint. What is the room's actual length?

    1. 24 feet
    2. 28 feet
    3. 32 feet
    4. 11.5 feet
    Show answer

    Answer: 28 feet

    3.5 inches × 8 feet/inch = 28 feet.

  2. A scale drawing has a scale factor of 1:50. If a door is 2 cm in the drawing, how tall is the actual door?

    1. 25 cm
    2. 100 cm
    3. 52 cm
    4. 0.04 cm
    Show answer

    Answer: 100 cm

    2 cm × 50 = 100 cm actual.

  3. On a map, 2 cm represents 15 km. Two towns are 75 km apart. How far apart are they on the map?

    1. 5 cm
    2. 8 cm
    3. 10 cm
    4. 37.5 cm
    Show answer

    Answer: 10 cm

    Set up proportion: 2 cm / 15 km = x cm / 75 km. Cross multiply: 15x = 150, so x = 10 cm.

  4. A model train uses a scale of 1:87. The actual locomotive is 17.4 m long. How long is the model in cm?

    1. 2 cm
    2. 20 cm
    3. 200 cm
    4. 0.2 cm
    Show answer

    Answer: 20 cm

    17.4 m ÷ 87 = 0.2 m = 20 cm.

  5. Which scale represents the greatest reduction?

    1. 1:5
    2. 1:100
    3. 1:25
    4. 1:10
    Show answer

    Answer: 1:100

    1:100 has the largest second number, meaning the real object is 100× larger than the drawing — the greatest reduction.

  6. A park is 200 m long and 150 m wide. A student draws it with a scale of 1 cm = 25 m. What are the drawing's dimensions?

    1. 8 cm × 6 cm
    2. 10 cm × 7.5 cm
    3. 5 cm × 4 cm
    4. 4 cm × 3 cm
    Show answer

    Answer: 8 cm × 6 cm

    200 m ÷ 25 = 8 cm for length; 150 m ÷ 25 = 6 cm for width. Dimensions: 8 cm × 6 cm.

  7. You can use cross multiplication to solve scale drawing proportion problems.

    Show answer

    Answer: True

    Setting up a proportion (drawing/scale = actual/1) and cross multiplying is the standard method for scale problems.

  8. A scale drawing of a car uses 1 cm = 0.5 m. The car is 4 m long. Its length in the drawing is _____ cm.

    Show answer

    Answer: 8

    4 m ÷ 0.5 m/cm = 8 cm.

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