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A radar system can detect objects up to a distance of 50 km. If it scans an area

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Question: A radar system can detect objects up to a distance of 50 km. If it scans an area of 20 km radius, what is the area it can cover? (2023)

Options:

  1. 1256 km²
  2. 314 km²
  3. 400 km²
  4. 500 km²

Correct Answer: 1256 km²

Exam Year: 2023

Solution: 

Area = π × r² = π × (20 km)² ≈ 1256 km²

A radar system can detect objects up to a distance of 50 km. If it scans an area

Practice Questions

Q1
A radar system can detect objects up to a distance of 50 km. If it scans an area of 20 km radius, what is the area it can cover? (2023)
  1. 1256 km²
  2. 314 km²
  3. 400 km²
  4. 500 km²

Questions & Step-by-Step Solutions

A radar system can detect objects up to a distance of 50 km. If it scans an area of 20 km radius, what is the area it can cover? (2023)
  • Step 1: Understand that the radar system can scan a circular area with a radius of 20 km.
  • Step 2: Recall the formula for the area of a circle, which is Area = π × r², where r is the radius.
  • Step 3: Substitute the radius (20 km) into the formula: Area = π × (20 km)².
  • Step 4: Calculate (20 km)², which is 400 km².
  • Step 5: Multiply 400 km² by π (approximately 3.14): Area ≈ 3.14 × 400 km².
  • Step 6: Perform the multiplication: Area ≈ 1256 km².
  • Area Calculation – The question tests the ability to calculate the area of a circle using the formula A = π × r², where r is the radius.
  • Understanding Radar Range – The question involves understanding the radar's detection range and how it relates to the area being scanned.
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