Finding the Area of a Circle: A Simple Explanation

If the radius of a circle is 7 cm, what is its area?

• A. 38.5 cm²
• B. 43.96 cm²
• C. 154 cm²
• D. 98 cm²

Answer: (C)

To find the area of a circle, the formula used is \( A = \pi r^2 \), where \( A \) represents the area and \( r \) is the radius of the circle. In this case, the radius given is 7 cm. First, calculate the radius squared: \[ r^2 = 7^2 = 49 \] Next, multiply the squared radius by \( \pi \): \[ A = \pi \times 49 \] Using an approximate value for \( \pi \) (3.14), we can calculate the area: \[ A \approx 3.14 \times 49 = 153.86 \, \text{cm}^2 \] When rounded to the nearest whole number, this gives approximately 154 cm². Therefore, the correct answer corresponds with the provided choice of 154 cm², confirming the calculation aligns with the mathematical principles for finding the area of a circle. This illustrates the importance of correctly applying the formula and handling numerical computations carefully.

Understanding the Area of a Circle

So, you’re prepping for the GED Math test, and one of the concepts tripping you up is finding the area of a circle? Don’t sweat it! It’s simpler than it sounds, and I’m here to guide you through it step by step.

What’s the Formula?

First things first, let’s talk about the formula you need to know:

Area (A) = π × r²

Where:

• A is the area of the circle

• π (Pi) is approximately 3.14

• r is the radius of the circle

Okay, let’s break this down a bit. The radius is the distance from the center of the circle to any point on its edge. For example, if someone asked you about your favorite pizza, the radius would be half the size of that round, cheesy goodness!

Example: Let’s Calculate!

Here’s a quick problem for you: If the radius of a circle is 7 cm, how do you find the area? Let’s walk through it together.

1. Find the radius squared:

• Radius = 7 cm

• Radius squared = 7² = 49

2. Multiply by π (Pi):

• Area = π × 49

• Using our trusty 3.14 for π gives you:

• A ≈ 3.14 × 49 = 153.86 cm²

• Rounded off? That’s about 154 cm²! 🎉

Why Does This Matter?

Getting familiar with this formula is super important — not just for your GED but for life too! Whether you’re shopping for a round table, planning a garden, or just doodling shapes, understanding how to calculate area comes in handy!

Tips for the GED

Here’s the thing: on the GED, you’ll find questions like this sprinkled throughout the math section. They’re not just testing your ability to memorize. No way! They want to see if you can apply what you know in a practical way.

• Practice makes perfect: Try solving more circle area problems to build confidence.

• Visualize it: Draw circles and label the radius. Seeing it can really help concepts stick.

Wrapping it Up

So, as you prepare, remember that brushing up on area calculations isn’t just another box to check off. It’s about plying skills that you’ll rely on in different avenues of life. Knowing how to calculate the area of a circle is just one valuable tool in your math toolbox.

Keep those formulas handy, and don’t hesitate to practice!

And remember, every great mathematician started just where you are right now, so keep at it! You've got this!