Scale Drawing Measurements

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Scale Drawing Measurements · Grade 7 · Worksheet 1

1. A scale drawing uses 1 cm : 400 m. If a building is 6.4 cm tall on the drawing, what is its actual height in meters? Answer: 2560 Solution: The scale is 1 cm : 400 m, meaning 1 cm on the drawing equals 400 m in reality. The building's height on the drawing is 6.4 cm. Multiply the drawing measurement by the scale factor: 6.4 × 400.
   Full step-by-step solution

   Step 1: The scale is 1 cm : 400 m, meaning 1 cm on the drawing equals 400 m in reality. Step 2: The building's height on the drawing is 6.4 cm. Step 3: Multiply the drawing measurement by the scale factor: 6.4 × 400. Step 4: 6.4 × 400 = 2560. Step 5: The actual height is 2560 meters. Answer: 2560

2. An architect is creating a scale drawing of a new office building. The actual building will be 12,800 feet tall. If the scale used is 1:1600, what is the height of the building in the scale drawing? Answer: 8 feet Solution: The scale 1:1600 means that 1 unit on the drawing represents 1600 units in real life. Identify the actual height. Actual height = 12,800 feet.
   Full step-by-step solution

   Step 1: Understand the scale meaning. The scale 1:1600 means that 1 unit on the drawing represents 1600 units in real life. Step 2: Identify the actual height. Actual height = 12,800 feet. Step 3: Set up the relationship. Let the drawing height be \( h \) feet. From the scale: Drawing height / Actual height = 1 / 1600 So: h / 12,800 = 1 / 1600 Step 4: Solve for \( h \). Multiply both sides by 12,800: h = (1 / 1600) * 12,800 Step 5: Simplify the calculation. First, 12,800 / 1600: Divide numerator and denominator by 100: 128 / 16 Now 128 ÷ 16 = 8. Step 6: State the final answer. So the height in the scale drawing is 8 feet.

3. A scale drawing of a triangular park uses a scale of 1 cm : 50 m. In the drawing, the triangle has a base of 6.8 cm and a height of 4.5 cm. What is the actual area of the park in square meters? Answer: 38250 Solution: Convert the base from drawing measurement to actual measurement Drawing base = 6.8 cm Scale: 1 cm = 50 m Actual base = 6.8 × 50 = 340 m Convert the height from drawing measurement to actual measurement Drawing height = 4.5 cm Scale: 1 cm = 50 m Actual height = 4.5 × 50 = 225 m Area of triangle =…
   Full step-by-step solution

   Step 1: Convert the base from drawing measurement to actual measurement Drawing base = 6.8 cm Scale: 1 cm = 50 m Actual base = 6.8 × 50 = 340 m Step 2: Convert the height from drawing measurement to actual measurement Drawing height = 4.5 cm Scale: 1 cm = 50 m Actual height = 4.5 × 50 = 225 m Step 3: Calculate the actual area of the triangular park Area of triangle = (base × height) ÷ 2 Area = (340 × 225) ÷ 2 Area = 76,500 ÷ 2 Area = 38,250 square meters The answer is 38250.

4. A scale drawing uses 1 cm : 40 m. If a park measures 12.5 cm on the drawing, what is its actual length in meters? Answer: 500 Solution: The scale is 1 cm : 40 m, meaning 1 cm on the drawing equals 40 m in reality. The park measures 12.5 cm on the drawing. Multiply the drawing length by the scale factor: 12.5 × 40 = 500.
   Full step-by-step solution

   Step 1: The scale is 1 cm : 40 m, meaning 1 cm on the drawing equals 40 m in reality. Step 2: The park measures 12.5 cm on the drawing. Step 3: Multiply the drawing length by the scale factor: 12.5 × 40 = 500. Step 4: The actual length of the park is 500 meters. The answer is 500.

5. Emma is creating a scale model of a cruise ship for her science project. The actual ship is 320 meters long and has a beam width of 36 meters. If Emma's model uses a scale of 1:800, what is the length of her model in centimeters? Answer: 40 Solution: The actual ship length is 320 meters and the scale is 1:800, meaning 1 unit on the model represents 800 units in reality.
   Full step-by-step solution

   Step 1: The actual ship length is 320 meters and the scale is 1:800, meaning 1 unit on the model represents 800 units in reality. Step 2: Calculate the model length in meters: 320 ÷ 800 = 0.4 meters Step 3: Convert meters to centimeters: 0.4 meters × 100 = 40 centimeters Step 4: The length of Emma's model is 40 centimeters.

6. Liam is creating a scale model of a skyscraper for his architecture project. The actual building is 450 meters tall, and Liam's model uses a scale of 1:1500. If the model's elevator shaft is represented by a thin rod that measures 18 centimeters in the model, what is the actual height of the elevator shaft in the real building? Answer: 270 Solution: The scale is 1:1500. This means 1 unit on the model represents 1500 units in reality. The elevator shaft in the model is 18 cm tall.
   Full step-by-step solution

   Let's go step by step. --- **Step 1: Understand the scale** The scale is 1:1500. This means 1 unit on the model represents 1500 units in reality. --- **Step 2: Interpret the given model measurement** The elevator shaft in the model is 18 cm tall. Let the actual height be \( H \) cm. From the scale: \[ \frac{\text{Model height}}{\text{Actual height}} = \frac{1}{1500} \] So: \[ \frac{18}{H} = \frac{1}{1500} \] --- **Step 3: Solve for actual height in cm** Cross-multiply: \[ 18 \times 1500 = H \] \[ H = 27000 \ \text{cm} \] --- **Step 4: Convert cm to meters** We know 1 m = 100 cm, so: \[ H = \frac{27000}{100} = 270 \ \text{m} \] --- **Step 5: Check with building height for consistency** Actual building height = 450 m. Model height in cm = \( \frac{450 \times 100}{1500} = \frac{45000}{1500} = 30 \) cm. So the model building is 30 cm tall. The elevator shaft in the model is 18 cm tall, which is \( \frac{18}{30} = 0.6 \) of the building's model height. 0.6 of the actual building height = \( 0.6 \times 450 = 270 \) m. Matches. --- **Final Answer:** 270

7. A scale drawing uses 1 cm : 40 m. If a playground measures 15 cm on the drawing, what is its actual length in meters? Answer: 600 Solution: Identify the scale ratio: 1 cm on the drawing = 40 m in reality. The playground measures 15 cm on the drawing. Multiply the drawing measurement by the scale factor: 15 cm × 40 m/cm.
   Full step-by-step solution

   Step 1: Identify the scale ratio: 1 cm on the drawing = 40 m in reality. Step 2: The playground measures 15 cm on the drawing. Step 3: Multiply the drawing measurement by the scale factor: 15 cm × 40 m/cm. Step 4: Calculate: 15 × 40 = 600. Step 5: The actual length is 600 meters.

8. A scale drawing uses 1 cm : 25 m. If a building is 8.4 cm tall in the drawing, what is its actual height in meters? Answer: 210 Solution: Identify the scale ratio: 1 cm on the drawing represents 25 m in reality. The building's height in the drawing is 8.4 cm. To find the actual height, multiply the drawing measurement by the scale factor: 8.4 cm × 25 m/cm.
   Full step-by-step solution

   Step 1: Identify the scale ratio: 1 cm on the drawing represents 25 m in reality. Step 2: The building's height in the drawing is 8.4 cm. Step 3: To find the actual height, multiply the drawing measurement by the scale factor: 8.4 cm × 25 m/cm. Step 4: Calculate: 8.4 × 25 = 210. Step 5: The actual height is 210 meters.

9. A scale drawing uses 1 cm : 120 m. If the distance between two points on the drawing is 7.5 cm, what is the actual distance in meters? Answer: 900 Solution: Identify the scale: 1 cm on the drawing = 120 m in reality. The drawing distance is 7.5 cm. Multiply the drawing distance by the scale factor: 7.5 × 120.
   Full step-by-step solution

   Step 1: Identify the scale: 1 cm on the drawing = 120 m in reality. Step 2: The drawing distance is 7.5 cm. Step 3: Multiply the drawing distance by the scale factor: 7.5 × 120. Step 4: Calculate: 7.5 × 120 = 900. Step 5: The actual distance is 900 meters.