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

A circle has a circumference of 31.41.

What is its radius?

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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