Aimathic – Scale drawings – Free Math Worksheets

Scale drawings

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Difficulty: 1 – 5

5108617

A photograph shows an ant at \(12\) times its actual size. The ant measures \(5.4\,\text{cm}\) in the photograph. What is the ant's actual length in millimeters?

Hints

- A magnification of \(12\) means the image length is \(12\) times the actual length. - Decide whether the actual ant should be longer or shorter than the image. - Convert centimeters to millimeters after finding the actual length.

Solution

1. Divide the image length by the scale factor: \(5.4\div12=0.45\,\text{cm}\). 2. Convert centimeters to millimeters: \(0.45\,\text{cm}=4.5\,\text{mm}\).

Answer

The ant is \(4.5\,\text{mm}\) long.

5164357

A small kitchen table is actually \(150\,\text{cm}\) long. In a scale drawing, it is \(15\,\text{cm}\) long. What scale was used?

Hints

- Compare the actual length with the drawing length. - Determine how many times the drawing length fits into the actual length. - Write the drawing-to-actual relationship as a scale.

Solution

1. Compare the actual length with the drawing length: \(150\,\text{cm} \div 15\,\text{cm} = 10\). 2. The actual table is \(10\) times as long as the drawing, so the scale is \(1{:}10\).

Answer

\(1{:}10\)

5108627

A microorganism is actually \(0.25\,\text{mm}\) long. a) How long does it appear under \(40\)-times magnification? Give the answer in centimeters. b) A student wants the image to be exactly \(2\,\text{cm}\) long. What magnification factor is needed?

Hints

- Relate actual length, image length, and magnification factor. - Use the same length unit before forming a scale factor. - For part b), compare the desired image length with the actual length.

Solution

1. For a), multiply the actual length by the scale factor: \(0.25\cdot40=10\,\text{mm}\). 2. Convert \(10\,\text{mm}\) to \(1\,\text{cm}\). 3. For b), convert the desired image length: \(2\,\text{cm}=20\,\text{mm}\). 4. Divide image length by actual length: \(20\div0.25=80\).

Answer

a) \(1\,\text{cm}\) b) \(80\)-times magnification

5108637

A technical part is only \(0.08\,\text{mm}\) thick. In a design drawing, it is shown as \(4\,\text{mm}\) thick. a) Find the scale factor of the drawing. b) A second part is \(0.12\,\text{mm}\) thick. How thick will it appear in the same drawing? c) If the first part is enlarged by a factor of \(1000\), how thick will it appear in centimeters?

Hints

- Compare the drawn thickness with the actual thickness to find the scale factor. - Apply the same scale factor to the second part. - Convert millimeters to centimeters after applying the factor in part c).

Solution

1. For a), divide drawing thickness by actual thickness: \(4\div0.08=50\). The scale factor is \(50\). 2. For b), apply the same factor: \(0.12\cdot50=6\,\text{mm}\). 3. For c), \(0.08\cdot1000=80\,\text{mm}=8\,\text{cm}\).

Answer

a) \(50\) b) \(6\,\text{mm}\) c) \(8\,\text{cm}\)

5208017

Three maps of a city use these scales: Map A: \(1:2000\) Map B: \(1:25{,}000\) Map C: \(1:250{,}000\) a) On which map does \(1\,\text{cm}\) represent the greatest actual distance? b) Which map is best for seeing details such as individual buildings and street names? Explain. c) How many meters does \(1\,\text{cm}\) represent on Map B?

Hints

- Compare the numbers after the colon. - A larger scale denominator means a larger actual area is compressed onto the map. - Convert centimeters to meters for c).

Solution

1. A larger denominator means a greater reduction. Therefore, \(1\,\text{cm}\) represents the greatest actual distance on Map C. 2. A smaller denominator shows objects at a larger size and with more detail. Therefore, Map A is best for individual buildings and street names. 3. On Map B, \(1\,\text{cm}\) represents \(25{,}000\,\text{cm}\). Convert to meters: \(25{,}000\div 100=250\,\text{m}\).

Answer

a) Map C b) Map A, because it has the least reduction and shows the most detail. c) \(250\,\text{m}\)

5208067

A school campus is \(200\,\text{m}\) long. It will be drawn using two scales. Drawing A uses \(1:1000\). Drawing B uses \(1:2500\). a) Find the campus length in each drawing, in centimeters. b) Which drawing shows the campus as a smaller image? Explain without doing another calculation.

Hints

- Convert the actual length to centimeters. - Divide by each scale denominator. - A larger denominator creates a smaller drawing.

Solution

1. Convert the actual length: \(200\,\text{m}=20{,}000\,\text{cm}\). 2. Drawing A has length \(20{,}000\div 1000=20\,\text{cm}\). 3. Drawing B has length \(20{,}000\div 2500=8\,\text{cm}\). 4. Drawing B is smaller because a larger scale denominator means a greater reduction.

Answer

a) Drawing A: \(20\,\text{cm}\) Drawing B: \(8\,\text{cm}\) b) Drawing B, because \(1:2500\) reduces the actual length more than \(1:1000\).

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