Use The Correct Formula To Find The Area Of A Circle If The Diameter Is 21 Mi. Round To The Nearest Tenth. Use 3.14 For $\pi$.A. 55.94 Mi 2 55.94 \, \text{mi}^2 55.94 Mi 2 B. 1 , 364.74 Mi 2 1,364.74 \, \text{mi}^2 1 , 364.74 Mi 2 C. 346.19 Mi 2 346.19 \, \text{mi}^2 346.19 Mi 2 D.

Introduction

In mathematics, the area of a circle is a fundamental concept that is used to calculate the space inside a circular shape. The formula to find the area of a circle is given by A = πr^2, where A is the area and r is the radius of the circle. However, in this article, we will be given the diameter of the circle, which is 21 miles. We will use the correct formula to find the area of the circle and round the answer to the nearest tenth.

Understanding the Formula

The formula to find the area of a circle is A = πr^2. However, we are given the diameter of the circle, which is 21 miles. To find the area, we need to first find the radius of the circle. The radius is half the diameter, so we can calculate the radius as follows:

r = diameter / 2 r = 21 / 2 r = 10.5 miles

Now that we have the radius, we can plug it into the formula to find the area:

A = πr^2 A = π(10.5)^2 A = 3.14(110.25) A = 346.19

Rounding to the Nearest Tenth

We are asked to round the answer to the nearest tenth. To do this, we need to look at the hundredth place, which is 9 in this case. Since 9 is greater than or equal to 5, we round up to the next tenth. Therefore, the area of the circle is approximately 346.2 miles^2.

Conclusion

In conclusion, we have used the correct formula to find the area of a circle given the diameter. We first found the radius by dividing the diameter by 2, and then plugged it into the formula to find the area. We rounded the answer to the nearest tenth, which is 346.2 miles^2.

Answer

The correct answer is C. 346.19 mi^2.

Why is this Important?

Understanding how to find the area of a circle is an important concept in mathematics. It has many real-world applications, such as calculating the area of a circular field, the surface area of a sphere, and the volume of a cylinder. It is also a fundamental concept in geometry and trigonometry.

Real-World Applications

The area of a circle has many real-world applications. For example:

• Calculating the area of a circular field to determine the amount of fertilizer or water needed.
• Calculating the surface area of a sphere to determine the amount of paint needed.
• Calculating the volume of a cylinder to determine the amount of liquid it can hold.

Tips and Tricks

Here are some tips and tricks to help you remember how to find the area of a circle:

• Always remember that the formula is A = πr^2.
• Make sure to find the radius by dividing the diameter by 2.
• Plug the radius into the formula to find the area.
• Round the answer to the nearest tenth.

Common Mistakes

Here are some common mistakes to avoid when finding the area of a circle:

• Forgetting to find the radius by dividing the diameter by 2.
• Plugging the diameter into the formula instead of the radius.
• Not rounding the answer to the nearest tenth.

Conclusion

Q: What is the formula to find the area of a circle?

A: The formula to find the area of a circle is A = πr^2, where A is the area and r is the radius of the circle.

Q: What is the radius of a circle?

A: The radius of a circle is the distance from the center of the circle to the edge. It is half the diameter of the circle.

Q: How do I find the radius of a circle if I know the diameter?

A: To find the radius of a circle if you know the diameter, simply divide the diameter by 2. For example, if the diameter is 21 miles, the radius would be 21 / 2 = 10.5 miles.

Q: What is the value of π?

A: The value of π is approximately 3.14. However, it can also be expressed as a decimal or a fraction.

Q: How do I round the answer to the nearest tenth?

A: To round the answer to the nearest tenth, look at the hundredth place. If it is 5 or greater, round up to the next tenth. If it is less than 5, round down to the previous tenth.

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

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

• Calculating the area of a circular field to determine the amount of fertilizer or water needed.
• Calculating the surface area of a sphere to determine the amount of paint needed.
• Calculating the volume of a cylinder to determine the amount of liquid it can hold.

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

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

• Forgetting to find the radius by dividing the diameter by 2.
• Plugging the diameter into the formula instead of the radius.
• Not rounding the answer to the nearest tenth.

Q: How do I remember the formula A = πr^2?

A: One way to remember the formula A = πr^2 is to think of it as "Area equals pi times radius squared." You can also use a mnemonic device such as "A is for Area, P is for Pi, R is for Radius, and 2 is for Squared."

Q: Can I use a calculator to find the area of a circle?

A: Yes, you can use a calculator to find the area of a circle. Simply enter the value of the radius and the value of π, and the calculator will give you the area.

Q: What if I don't know the value of π?

A: If you don't know the value of π, you can use an approximation such as 3.14. However, if you need a more accurate value, you can use a calculator or a mathematical table to find the value of π.

Q: Can I find the area of a circle if I know the circumference?

A: Yes, you can find the area of a circle if you know the circumference. The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius. You can rearrange this formula to solve for the radius, and then use the formula A = πr^2 to find the area.