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If the radius of a circle is tripled, how does the area change? (2019)

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Question: If the radius of a circle is tripled, how does the area change? (2019)

Options:

  1. Increases by 3 times
  2. Increases by 6 times
  3. Increases by 9 times
  4. Remains the same

Correct Answer: Increases by 9 times

Exam Year: 2019

Solution: 

Area = πr². If radius is tripled, new area = π(3r)² = 9πr², which is 9 times the original area.

If the radius of a circle is tripled, how does the area change? (2019)

Practice Questions

Q1
If the radius of a circle is tripled, how does the area change? (2019)
  1. Increases by 3 times
  2. Increases by 6 times
  3. Increases by 9 times
  4. Remains the same

Questions & Step-by-Step Solutions

If the radius of a circle is tripled, how does the area change? (2019)
  • Step 1: Understand the formula for the area of a circle, which is Area = πr².
  • Step 2: Identify the original radius of the circle as 'r'.
  • Step 3: If the radius is tripled, the new radius becomes '3r'.
  • Step 4: Substitute the new radius into the area formula: Area = π(3r)².
  • Step 5: Calculate (3r)², which equals 9r².
  • Step 6: Now, substitute this back into the area formula: Area = π(9r²).
  • Step 7: This simplifies to Area = 9πr².
  • Step 8: Compare the new area (9πr²) to the original area (πr²).
  • Step 9: Conclude that the new area is 9 times the original area.
  • Area of a Circle – Understanding the formula for the area of a circle (A = πr²) and how changes in the radius affect the area.
  • Scaling Effects – Recognizing how scaling the radius by a factor affects the area, specifically that area scales with the square of the radius.
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