Type The Correct Answer In The Box. Use Numerals Instead Of Words.Rob And His Brother Are Riding In The Same Car On A Ferris Wheel Which Has A Diameter Of 40 Feet. Once The Ferris Wheel Starts, They Travel A Distance Of $\frac{85}{3} \pi$ Feet

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Introduction

In this problem, we are given the diameter of a Ferris wheel and the distance traveled by Rob and his brother as they ride in the same car. We need to find the correct answer in the box, using numerals instead of words. This problem involves the concept of circumference, which is an essential topic in mathematics.

Understanding Circumference

The circumference of a circle is the distance around the circle. It is calculated using the formula: C = 2Ï€r, where C is the circumference and r is the radius of the circle. Since we are given the diameter of the Ferris wheel, we can find the radius by dividing the diameter by 2.

Given Information

  • Diameter of the Ferris wheel: 40 feet
  • Distance traveled by Rob and his brother: 853Ï€\frac{85}{3} \pi feet

Step 1: Find the Radius of the Ferris Wheel

To find the radius of the Ferris wheel, we need to divide the diameter by 2.

diameter = 40
radius = diameter / 2
print(radius)

Step 2: Calculate the Circumference of the Ferris Wheel

Now that we have the radius, we can calculate the circumference using the formula: C = 2Ï€r.

import math
circumference = 2 * math.pi * radius
print(circumference)

Step 3: Compare the Circumference with the Distance Traveled

We are given the distance traveled by Rob and his brother, which is 853Ï€\frac{85}{3} \pi feet. We need to compare this distance with the circumference of the Ferris wheel.

Solution

Let's calculate the circumference of the Ferris wheel using the formula: C = 2Ï€r.

import math
diameter = 40
radius = diameter / 2
circumference = 2 * math.pi * radius
print(circumference)

The circumference of the Ferris wheel is approximately 251.327 feet.

Now, let's compare this distance with the distance traveled by Rob and his brother.

import math
distance_traveled = (85/3) * math.pi
print(distance_traveled)

The distance traveled by Rob and his brother is approximately 236.62 feet.

Conclusion

Based on the calculations, we can see that the distance traveled by Rob and his brother is less than the circumference of the Ferris wheel. This makes sense, as they are traveling a certain distance around the wheel, but not the entire circumference.

Answer

The correct answer is: 251.327

Note: The answer is in the box, using numerals instead of words.

Discussion

This problem involves the concept of circumference, which is an essential topic in mathematics. The circumference of a circle is the distance around the circle, and it is calculated using the formula: C = 2Ï€r. In this problem, we were given the diameter of the Ferris wheel and the distance traveled by Rob and his brother. We needed to find the correct answer in the box, using numerals instead of words.

Related Topics

  • Circumference of a circle
  • Diameter of a circle
  • Radius of a circle
  • Distance traveled around a circle

Practice Problems

  • Find the circumference of a circle with a diameter of 30 feet.
  • Find the distance traveled around a circle with a radius of 10 feet.
  • Find the circumference of a circle with a radius of 15 feet.

Conclusion

In this problem, we learned how to calculate the circumference of a Ferris wheel using the formula: C = 2Ï€r. We also compared the circumference with the distance traveled by Rob and his brother. This problem involves the concept of circumference, which is an essential topic in mathematics.

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Q: What is the circumference of a circle?

A: The circumference of a circle is the distance around the circle. It is calculated using the formula: C = 2Ï€r, where C is the circumference and r is the radius of the circle.

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

A: To calculate the circumference of a circle, you need to know the radius of the circle. You can use the formula: C = 2Ï€r, where C is the circumference and r is the radius of the circle.

Q: What is the difference between the circumference and the diameter of a circle?

A: The circumference of a circle is the distance around the circle, while the diameter of a circle is the distance across the circle, passing through its center. The circumference is always longer than the diameter.

Q: Can I use the diameter to calculate the circumference of a circle?

A: Yes, you can use the diameter to calculate the circumference of a circle. Since the diameter is twice the radius, you can use the formula: C = πd, where C is the circumference and d is the diameter of the circle.

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 the radius increases, the circumference also increases.

Q: Can I use the circumference to calculate the radius of a circle?

A: Yes, you can use the circumference to calculate the radius of a circle. Since the circumference is equal to 2Ï€r, you can rearrange the formula to solve for r: r = C / (2Ï€).

Q: What is the significance of the value π in the formula for circumference?

A: The value π is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. It is approximately equal to 3.14.

Q: Can I use a calculator to calculate the circumference of a circle?

A: Yes, you can use a calculator to calculate the circumference of a circle. Simply enter the value of the radius or diameter, and the calculator will give you the circumference.

Q: What are some real-world applications of the concept of circumference?

A: The concept of circumference has many real-world applications, including:

  • Calculating the distance around a circle or an ellipse
  • Determining the length of a circular path or a road
  • Finding the perimeter of a circular object or a shape
  • Calculating the area of a circle or an ellipse

Q: Can I use the concept of circumference to solve problems in other areas of mathematics?

A: Yes, you can use the concept of circumference to solve problems in other areas of mathematics, including:

  • Geometry: to calculate the perimeter and area of circles and ellipses
  • Trigonometry: to calculate the length of sides and angles of triangles
  • Calculus: to calculate the area and volume of circles and ellipses

Q: What are some common mistakes to avoid when calculating the circumference of a circle?

A: Some common mistakes to avoid when calculating the circumference of a circle include:

  • Using the wrong formula (e.g. using C = Ï€d instead of C = 2Ï€r)
  • Forgetting to square the radius (e.g. using r^2 instead of r)
  • Using an incorrect value for Ï€ (e.g. using 3.0 instead of 3.14)
  • Not checking the units of the answer (e.g. using feet instead of meters)