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If the area of a circle is 50π, what is the radius?

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Question: If the area of a circle is 50π, what is the radius?

Options:

  1. 5
  2. 10
  3. 25
  4. 20

Correct Answer: 10

Solution: 

Area = πr^2 => 50π = πr^2 => r^2 = 50 => r = √50 = 5√2.

If the area of a circle is 50π, what is the radius?

Practice Questions

Q1
If the area of a circle is 50π, what is the radius?
  1. 5
  2. 10
  3. 25
  4. 20

Questions & Step-by-Step Solutions

If the area of a circle is 50π, what is the radius?
  • Step 1: Write down the formula for the area of a circle, which is Area = πr^2.
  • Step 2: Substitute the given area (50π) into the formula: 50π = πr^2.
  • Step 3: To simplify, divide both sides of the equation by π: 50 = r^2.
  • Step 4: Now, to find the radius (r), take the square root of both sides: r = √50.
  • Step 5: Simplify √50. Since 50 can be broken down into 25 and 2, we have √50 = √(25 * 2) = √25 * √2 = 5√2.
  • Area of a Circle – The area of a circle is calculated using the formula A = πr², where A is the area and r is the radius.
  • Square Roots – Finding the radius involves taking the square root of the area divided by π.
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