The Circumference Of A Circular Pond In The Park Is 120 Meters. Find The Area.1. The Formula For Circumference Is C = Π D C = \pi D C = Π D . - What Is The Value Of The Diameter Rounded To The Nearest Whole Number? $\square$2. What Is The Value Of

Introduction

In this article, we will explore the relationship between the circumference and area of a circular pond in a park. Given that the circumference of the pond is 120 meters, we will use the formula for circumference to find the diameter and then calculate the area of the pond.

The Formula for Circumference

The formula for the circumference of a circle is given by:

$$C = \pi d$$

where $C$ is the circumference, $\pi$ is a mathematical constant approximately equal to 3.14, and $d$ is the diameter of the circle.

Finding the Diameter

We are given that the circumference of the pond is 120 meters. Using the formula for circumference, we can set up an equation to solve for the diameter:

$$120 = \pi d$$

To solve for $d$, we can divide both sides of the equation by $\pi$:

$$d = \frac{120}{\pi}$$

Using a calculator, we can find the value of $d$:

$$d \approx \frac{120}{3.14} \approx 38.19$$

Rounding to the nearest whole number, we get:

$$d \approx 38$$

The Value of the Diameter

So, the value of the diameter rounded to the nearest whole number is:

38

Finding the Area

Now that we have found the diameter, we can use the formula for the area of a circle to find the area of the pond:

$$A = \pi r^2$$

where $A$ is the area, $\pi$ is a mathematical constant approximately equal to 3.14, and $r$ is the radius of the circle.

Since we know the diameter, we can find the radius by dividing the diameter by 2:

$$r = \frac{d}{2} = \frac{38}{2} = 19$$

Now, we can plug in the value of $r$ into the formula for area:

$$A = \pi (19)^2$$

Using a calculator, we can find the value of $A$:

$$A \approx 3.14 \times 361 \approx 1133.14$$

So, the area of the pond is approximately:

1133.14 square meters

Conclusion

In this article, we used the formula for circumference to find the diameter of a circular pond in a park, and then used the formula for area to find the area of the pond. We found that the diameter is approximately 38 meters and the area is approximately 1133.14 square meters.

Discussion

This problem is a great example of how to use the formula for circumference to find the diameter of a circle, and then use the formula for area to find the area of the circle. It also highlights the importance of rounding numbers to the nearest whole number when working with real-world measurements.

Real-World Applications

This problem has many real-world applications, such as:

• Finding the area of a circular pond or lake
• Calculating the area of a circular garden or park
• Determining the area of a circular swimming pool or hot tub

Mathematical Concepts

This problem involves the following mathematical concepts:

• Circumference of a circle
• Diameter of a circle
• Area of a circle
• Rounding numbers to the nearest whole number

Tips and Tricks

Here are some tips and tricks for solving this problem:

• Make sure to use the correct formula for circumference and area
• Use a calculator to find the value of $\pi$
• Round numbers to the nearest whole number when working with real-world measurements
• Check your work by plugging in the values into the formulas and making sure they are correct.
  The Circumference of a Circular Pond: Q&A =============================================

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

A: The formula for the circumference of a circle is given by:

$$C = \pi d$$

where $C$ is the circumference, $\pi$ is a mathematical constant approximately equal to 3.14, and $d$ is the diameter of the circle.

Q: How do I find the diameter of a circle given its circumference?

A: To find the diameter of a circle given its circumference, you can use the formula for circumference and solve for $d$:

$$d = \frac{C}{\pi}$$

Q: What is the value of the diameter of the circular pond in the park?

A: The value of the diameter of the circular pond in the park is approximately 38 meters, rounded to the nearest whole number.

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

A: To find the area of a circle given its diameter, you can use the formula for area and solve for $A$:

$$A = \pi r^2$$

where $r$ is the radius of the circle. Since you know the diameter, you can find the radius by dividing the diameter by 2:

$$r = \frac{d}{2}$$

Q: What is the area of the circular pond in the park?

A: The area of the circular pond in the park is approximately 1133.14 square meters.

Q: Why is it important to round numbers to the nearest whole number when working with real-world measurements?

A: Rounding numbers to the nearest whole number is important when working with real-world measurements because it helps to simplify the calculations and make them more manageable. It also helps to reduce the risk of errors and make the results more accurate.

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

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

• Finding the area of a circular pond or lake
• Calculating the area of a circular garden or park
• Determining the area of a circular swimming pool or hot tub
• Finding the circumference of a circular road or highway
• Calculating the area of a circular building or structure

Q: What are some mathematical concepts that are involved in finding the circumference and area of a circle?

A: Some mathematical concepts that are involved in finding the circumference and area of a circle include:

• Circumference of a circle
• Diameter of a circle
• Area of a circle
• Rounding numbers to the nearest whole number
• Using the formula for circumference and area

Q: How can I use a calculator to find the value of $\pi$?

A: You can use a calculator to find the value of $\pi$ by typing in the command "pi" or using the calculator's built-in function to find the value of $\pi$.

Q: What are some tips and tricks for solving problems involving the circumference and area of a circle?

A: Some tips and tricks for solving problems involving the circumference and area of a circle include:

• Make sure to use the correct formula for circumference and area
• Use a calculator to find the value of $\pi$
• Round numbers to the nearest whole number when working with real-world measurements
• Check your work by plugging in the values into the formulas and making sure they are correct.