Calculate Circle Area: Given Radius of 3 Units and Center O

Circle Area with Known Radius

O is the center of the circle in the diagram below.

What is its area?

333OOO

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the area of the circle
00:03 We will use the formula to calculate the area of a circle
00:08 We will substitute the radius value according to the given data and solve to find the area
00:25 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

O is the center of the circle in the diagram below.

What is its area?

333OOO

2

Step-by-step solution

Remember that the formula for the area of a circle is

πR²

We insert the known data:

π3²

π9

3

Final Answer

9π 9\pi cm²

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area of a circle equals π times radius squared
  • Technique: Substitute r = 3 into A = πr² to get π(3)²
  • Check: 3² = 9, so π × 9 = 9π square units ✓

Common Mistakes

Avoid these frequent errors
  • Using diameter instead of radius in the formula
    Don't substitute diameter into A = πr² = π(6)² = 36π! The diagram shows radius = 3, not diameter = 3. Always identify whether the given measurement is radius or diameter first.

Practice Quiz

Test your knowledge with interactive questions

The center of the circle in the diagram is O.

What is the area of the circle?

555OOO

FAQ

Everything you need to know about this question

How do I know if 3 is the radius or diameter?

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Look at the diagram carefully! The line from center O to the edge is labeled "3" - this is the radius because it goes from center to circumference.

Why do we use π instead of 3.14?

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Using π gives the exact answer! Writing 9π 9\pi is more precise than 28.26, and many math problems expect the exact form.

What does the ² mean in the formula?

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The ² means squared or "times itself". So r² = r × r. When r = 3, then r² = 3 × 3 = 9.

Do I need to include units in my answer?

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Yes! Since we're measuring area, use square units like cm², m², or just "square units" if no specific unit is given.

What if I calculated 18π instead?

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You might have used the circumference formula C = 2πr by mistake! Remember: circumference uses 2πr, but area uses πr².

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