Calculate Circle Area: Finding Area When Radius = 7

Circle Area with Perfect Square Radius

Look at the circle in the figure:

777

The radius is equal to 7.

What is the area of the circle?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's find the area of the circle.
00:08 We need the radius size from the data we have.
00:12 We will use the formula: area equals pi times radius squared.
00:17 Now, plug in the radius value and calculate the area.
00:21 And that's how we solve the problem! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the circle in the figure:

777

The radius is equal to 7.

What is the area of the circle?

2

Step-by-step solution

Remember that the formula for the area of a circle is

πR²

 

We replace the data we know:

π7²

π49

3

Final Answer

49π

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area of circle equals πr2 \pi r^2 where r is radius
  • Technique: Substitute r = 7 to get π×72=49π \pi \times 7^2 = 49\pi
  • Check: Verify 7² = 49, so area = 49π square units ✓

Common Mistakes

Avoid these frequent errors
  • Using radius instead of radius squared
    Don't calculate π × 7 = 7π! This forgets to square the radius and gives a much smaller answer. The area formula requires r², not just r. Always square the radius first: π × 7² = 49π.

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

Why do we square the radius in the area formula?

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Area measures two-dimensional space, so we need to multiply length × width. For a circle, we use πr2 \pi r^2 because it's like fitting r × r squares inside the circle, adjusted by π.

What's the difference between area and circumference?

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Area is the space inside (π r²), while circumference is the distance around the edge (2π r). Area uses r², circumference uses r.

Do I need to calculate the exact decimal value of 49π?

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Usually no! Leaving your answer as 49π is exact and preferred in most math problems. Only calculate the decimal if specifically asked.

How do I remember that 7² equals 49?

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Practice your perfect squares! 7 × 7 = 49 is a key multiplication fact. You can also think: 7² = (5+2)² but direct memorization is faster.

What if the radius was a fraction like 3.5?

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Same formula! If r = 3.5, then area = π × (3.5)² = π × 12.25 = 12.25π 12.25\pi square units.

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