Examkin

Question

Difficulty: MediumScale Drawings

A maritime authority is reviewing a nautical chart to designate a restricted sailing zone. The chart uses a scale where 12 inch\frac{1}{2}\text{ inch} represents 30 nautical miles30\text{ nautical miles}. If the restricted zone is drawn as a rectangle measuring 2 inches2\text{ inches} by 3 inches3\text{ inches} on the chart, what is the actual area of the restricted zone in square nautical miles?

  1. A
    360
  2. B
    1,350
  3. 21,600Answer
  4. D
    2,160

Answer

21,600
The correct answer is found by first converting each chart dimension into its actual distance. Because a half inch represents 30 nautical miles, one full inch represents 60 nautical miles. Multiplying the chart's 2-inch and 3-inch dimensions by 60 yields actual dimensions of 120 and 180 nautical miles. Multiplying these true dimensions together gives a final area of 21,600 square nautical miles.

Step-by-Step Solution

1
Determine the linear scale for a full inch based on the provided fractional scale.
Since 1/2 inch=30 nautical miles1/2\text{ inch} = 30\text{ nautical miles}, then 1 inch=60 nautical miles1\text{ inch} = 60\text{ nautical miles}.
Establishing the unit rate for 1 inch simplifies the conversion of the chart dimensions.
2
Convert the chart dimensions to actual dimensions.
Width: 2 inches×60=120 nautical miles2\text{ inches} \times 60 = 120\text{ nautical miles}. Length: 3 inches×60=180 nautical miles3\text{ inches} \times 60 = 180\text{ nautical miles}.
Linear dimensions must be converted to actual lengths before computing the true area.
3
Calculate the actual area by multiplying the actual length and actual width.
120×180=21,600 square nautical miles120 \times 180 = 21,600\text{ square nautical miles}.
The area of a rectangle is the product of its length and width.

Key Concept

Calculating true area from a scale drawing by converting linear dimensions first.
Rate this question

Topics

Scale Drawings

More questions from this topic