The Radius Of A Circle Is 17 Meters. What Is The Circle's Circumference? Use $\pi \approx 3.14$ And Round Your Answer To The Nearest Hundredth.

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Understanding the Problem

The problem requires us to find the circumference of a circle given its radius. The radius of the circle is provided as 17 meters. To find the circumference, we will use the formula for the circumference of a circle, which is given by C = 2πr, where C is the circumference and r is the radius.

Formula for Circumference

The formula for the circumference of a circle is C = 2πr. This formula is derived from the fact that the circumference of a circle is equal to the distance around the circle. The distance around a circle can be calculated by adding up the lengths of an infinite number of infinitesimally small line segments that make up the circle. This can be represented mathematically as the integral of the differential of the arc length, which is equal to 2πr.

Calculating the Circumference

To calculate the circumference of the circle, we will substitute the given value of the radius (17 meters) into the formula C = 2πr. We will also use the approximation π ≈ 3.14.

import math

# Define the radius of the circle
radius = 17

# Define the value of pi
pi = 3.14

# Calculate the circumference
circumference = 2 * pi * radius

# Round the answer to the nearest hundredth
circumference = round(circumference, 2)

print("The circumference of the circle is:", circumference, "meters")

Rounding the Answer

The calculated value of the circumference will be a decimal value. To round the answer to the nearest hundredth, we will use the round() function in Python.

Final Answer

The final answer is the rounded value of the circumference, which is 106.78 meters.

Conclusion

In this problem, we used the formula for the circumference of a circle (C = 2πr) to find the circumference of a circle with a radius of 17 meters. We used the approximation π ≈ 3.14 and rounded the answer to the nearest hundredth. The final answer is 106.78 meters.

Real-World Applications

The formula for the circumference of a circle has many real-world applications. For example, it can be used to calculate the distance around a circular track or the perimeter of a circular plot of land. It can also be used to calculate the length of a circular wire or the circumference of a circular pipe.

Example Problems

Here are a few example problems that involve finding the circumference of a circle:

  • Find the circumference of a circle with a radius of 10 meters.
  • Find the circumference of a circle with a radius of 25 meters.
  • Find the circumference of a circle with a radius of 50 meters.

Solutions to Example Problems

Here are the solutions to the example problems:

  • The circumference of a circle with a radius of 10 meters is 62.80 meters.
  • The circumference of a circle with a radius of 25 meters is 157.08 meters.
  • The circumference of a circle with a radius of 50 meters is 314.16 meters.

Summary

In this article, we used the formula for the circumference of a circle (C = 2πr) to find the circumference of a circle with a radius of 17 meters. We used the approximation π ≈ 3.14 and rounded the answer to the nearest hundredth. The final answer is 106.78 meters. We also discussed the real-world applications of the formula and provided solutions to example problems.

Understanding the Problem

The problem requires us to find the circumference of a circle given its radius. The radius of the circle is provided as 17 meters. To find the circumference, we will use the formula for the circumference of a circle, which is given by C = 2πr, where C is the circumference and r is the radius.

Q&A

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

A: The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius.

Q: What is the value of π used in the formula?

A: The value of π used in the formula is approximately 3.14.

Q: How do I calculate the circumference of a circle?

A: To calculate the circumference of a circle, you need to substitute the given value of the radius into the formula C = 2πr and use the approximation π ≈ 3.14.

Q: What is the circumference of a circle with a radius of 17 meters?

A: The circumference of a circle with a radius of 17 meters is 106.78 meters.

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

A: To round the answer to the nearest hundredth, you can use the round() function in Python or simply look at the second decimal place and round up or down accordingly.

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

A: The formula for the circumference of a circle has many real-world applications, such as calculating the distance around a circular track or the perimeter of a circular plot of land.

Q: Can I use the formula for the circumference of a circle to find the radius of a circle?

A: No, the formula for the circumference of a circle is used to find the circumference given the radius, not the radius given the circumference.

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

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

Q: What is the relationship between the circumference and the radius of a circle?

A: The circumference of a circle is directly proportional to the radius of the circle, as shown by the formula C = 2πr.

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

A: Yes, the diameter of a circle is twice the radius, so you can use the formula C = 2πr to find the diameter by dividing the circumference by π and then multiplying by 2.

Example Problems and Solutions

Here are a few example problems and their solutions:

Example Problem 1

Find the circumference of a circle with a radius of 10 meters.

Solution: The circumference of a circle with a radius of 10 meters is 62.80 meters.

Example Problem 2

Find the circumference of a circle with a radius of 25 meters.

Solution: The circumference of a circle with a radius of 25 meters is 157.08 meters.

Example Problem 3

Find the circumference of a circle with a radius of 50 meters.

Solution: The circumference of a circle with a radius of 50 meters is 314.16 meters.

Conclusion

In this article, we used the formula for the circumference of a circle (C = 2πr) to find the circumference of a circle with a radius of 17 meters. We also answered some frequently asked questions about the formula and provided solutions to example problems.