Find The Radius Of A Circle With An Area Of 380.1 Cm². Round Your Answer To The Nearest Centimeter.A. 11 Cm B. 10 Cm C. 9 Cm D. 12 Cm

by ADMIN 139 views

Introduction

In geometry, a circle is a set of points that are all equidistant from a central point called the center. The distance from the center to any point on the circle is called the radius. In this article, we will explore how to find the radius of a circle given its area. We will use the formula for the area of a circle, which is A = πr², where A is the area and r is the radius.

The Formula for the Area of a Circle

The formula for the area of a circle is A = πr², where A is the area and r is the radius. This formula is derived from the fact that the area of a circle is equal to the product of the radius squared and the constant pi (π).

Finding the Radius of a Circle

To find the radius of a circle, we can rearrange the formula for the area of a circle to solve for the radius. We can do this by dividing both sides of the equation by π and then taking the square root of both sides.

A = πr² r² = A / π r = √(A / π)

Example Problem

Find the radius of a circle with an area of 380.1 cm². Round your answer to the nearest centimeter.

Step 1: Plug in the Value of the Area

The area of the circle is given as 380.1 cm². We can plug this value into the formula for the radius.

r = √(380.1 / π)

Step 2: Calculate the Value of the Radius

Now that we have plugged in the value of the area, we can calculate the value of the radius.

r = √(380.1 / π) r = √(380.1 / 3.14159) r = √120.32 r ≈ 10.98

Step 3: Round the Answer to the Nearest Centimeter

The problem asks us to round our answer to the nearest centimeter. We can do this by rounding the value of the radius to the nearest whole number.

r ≈ 10.98 r ≈ 11

Conclusion

In this article, we have explored how to find the radius of a circle given its area. We have used the formula for the area of a circle, which is A = πr², and rearranged it to solve for the radius. We have then applied this formula to an example problem to find the radius of a circle with an area of 380.1 cm². Our answer is 11 cm.

Answer

The correct answer is A. 11 cm.

Additional Tips and Tricks

  • Make sure to use the correct value of pi (π) in your calculations.
  • Use a calculator to simplify your calculations.
  • Round your answer to the nearest centimeter as required by the problem.

Common Mistakes to Avoid

  • Make sure to plug in the correct value of the area into the formula.
  • Make sure to use the correct value of pi (π) in your calculations.
  • Avoid rounding errors by using a calculator to simplify your calculations.

Real-World Applications

The formula for the area of a circle has many real-world applications. For example, it can be used to find the area of a circular room, a circular table, or a circular pipe. It can also be used to find the radius of a circle given its area, which is useful in many fields such as engineering, architecture, and design.

Conclusion

Q: What is the formula for the area of a circle?

A: The formula for the area of a circle is A = πr², where A is the area and r is the radius.

Q: How do I find the radius of a circle given its area?

A: To find the radius of a circle given its area, you can rearrange the formula for the area of a circle to solve for the radius. You can do this by dividing both sides of the equation by π and then taking the square root of both sides.

r² = A / π r = √(A / π)

Q: What is the value of pi (π) that I should use in my calculations?

A: The value of pi (π) that you should use in your calculations is approximately 3.14159.

Q: How do I round my answer to the nearest centimeter?

A: To round your answer to the nearest centimeter, you can simply round the value of the radius to the nearest whole number.

Q: What are some common mistakes to avoid when finding the radius of a circle?

A: Some common mistakes to avoid when finding the radius of a circle include:

  • Plugging in the wrong value of the area into the formula
  • Using the wrong value of pi (π) in your calculations
  • Rounding errors due to incorrect rounding

Q: What are some real-world applications of the formula for the area of a circle?

A: Some real-world applications of the formula for the area of a circle include:

  • Finding the area of a circular room, a circular table, or a circular pipe
  • Finding the radius of a circle given its area, which is useful in many fields such as engineering, architecture, and design

Q: Can I use a calculator to simplify my calculations?

A: Yes, you can use a calculator to simplify your calculations. In fact, using a calculator can help you avoid rounding errors and ensure that your calculations are accurate.

Q: What if I have a negative value for the area of the circle?

A: If you have a negative value for the area of the circle, it means that the circle does not exist. The area of a circle cannot be negative, so you should check your calculations to ensure that you have entered the correct values.

Q: Can I use the formula for the area of a circle to find the diameter of a circle?

A: Yes, you can use the formula for the area of a circle to find the diameter of a circle. The diameter of a circle is twice the radius, so you can find the diameter by multiplying the radius by 2.

Conclusion

In conclusion, finding the radius of a circle given its area is a simple yet important concept in geometry. By using the formula for the area of a circle and rearranging it to solve for the radius, we can find the radius of a circle with ease. We have answered some frequently asked questions about finding the radius of a circle and provided some tips and tricks to help you avoid common mistakes.