Circles Worksheet Day #1 Answer Key: Quick Solutions
Table of Contents :
In this article, we will be discussing the answer key for the Circles Worksheet Day #1. Whether you're a teacher looking for quick solutions or a student eager to check your work, this guide will provide clear answers and explanations for each question. Let's dive in and explore the essential concepts surrounding circles while providing quick solutions to the problems presented in the worksheet. 📏🟠
Understanding Circles
Before we jump into the solutions, it’s essential to grasp the fundamental concepts of circles. A circle is defined as the set of all points in a plane that are equidistant from a given point called the center. The distance from the center to any point on the circle is known as the radius (r), while the distance across the circle passing through the center is the diameter (d), which is twice the radius.
Key Formulas
- Circumference (C): The distance around the circle.
- Formula: ( C = 2\pi r ) or ( C = \pi d )
- Area (A): The space enclosed by the circle.
- Formula: ( A = \pi r^2 )
Understanding these formulas is crucial for solving any problem related to circles. Now let’s look at the answers to the worksheet questions.
Circles Worksheet Day #1 Answer Key
Below is the answer key for the first day's worksheet. Each answer is accompanied by a brief explanation to help solidify your understanding.
<table> <tr> <th>Question Number</th> <th>Question</th> <th>Answer</th> <th>Explanation</th> </tr> <tr> <td>1</td> <td>Find the radius if the circumference is 31.4 cm.</td> <td>5 cm</td> <td>Using the formula ( C = 2\pi r ), we get ( r = \frac{C}{2\pi} = \frac{31.4}{2\pi} = 5 ).</td> </tr> <tr> <td>2</td> <td>Calculate the area of a circle with a radius of 7 cm.</td> <td>153.94 cm²</td> <td>Using ( A = \pi r^2 ), we find ( A = \pi (7^2) = 49\pi \approx 153.94 ).</td> </tr> <tr> <td>3</td> <td>If the diameter is 10 cm, what is the circumference?</td> <td>31.4 cm</td> <td>Using ( C = \pi d ), we have ( C = \pi (10) \approx 31.4 ).</td> </tr> <tr> <td>4</td> <td>What is the area of a circle with a diameter of 14 cm?</td> <td>153.94 cm²</td> <td>First, find the radius ( r = \frac{d}{2} = 7 ) cm, then use ( A = \pi r^2 = 49\pi \approx 153.94 ).</td> </tr> <tr> <td>5</td> <td>Calculate the circumference of a circle with a radius of 2.5 m.</td> <td>15.7 m</td> <td>Using ( C = 2\pi r ), we calculate ( C = 2\pi (2.5) \approx 15.7 ).</td> </tr> <tr> <td>6</td> <td>Find the radius of a circle with an area of 78.5 cm².</td> <td>5 cm</td> <td>Using ( A = \pi r^2 ), we solve for ( r = \sqrt{\frac{A}{\pi}} = \sqrt{\frac{78.5}{\pi}} \approx 5 ).</td> </tr> </table>
Important Notes
“Understanding the relationship between the radius, diameter, circumference, and area is key to mastering circle-related problems.”
Additional Practice
After checking your answers with the key, it’s crucial to continue practicing. Here are a few additional problems you can work on:
- A circle has a radius of 10 cm. What is its area?
- Find the circumference of a circle with a diameter of 4.5 m.
- If the area of a circle is 50.24 m², what is the radius?
Working on these additional problems will enhance your understanding of circles and improve your problem-solving skills. 🌟
Conclusion
Working with circles can initially seem daunting, but with a solid understanding of the key formulas and concepts, you can tackle any related problem with confidence. Use the provided answer key as a resource for verification and learning. Continue practicing with different problems to strengthen your comprehension, and soon, you'll find yourself navigating through circle problems effortlessly. Happy learning! ✏️🌍