Q. 2 What Is The Distance Covered By A Tire With A Radius Of 35 Cm In 15 Rotations? How Many Rotations Will A Tire With A Radius Of 10 Cm Require To Travel The Same Distance?\[$\left(\pi=\frac{22}{7}\right)\$\]

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Introduction

In this problem, we are tasked with finding the distance covered by a tire with a radius of 35 cm in 15 rotations. Additionally, we need to determine how many rotations a tire with a radius of 10 cm will require to travel the same distance. To solve this problem, we will use the concept of the circumference of a circle and the relationship between the radius and the circumference.

Circumference of a Circle

The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius of the circle. In this problem, we are given the radius of the tire as 35 cm. We can use this formula to find the circumference of the tire.

Calculating the Circumference

Using the formula C = 2πr, we can calculate the circumference of the tire with a radius of 35 cm.

import math

# Define the radius of the tire
radius = 35  # in cm

# Calculate the circumference
circumference = 2 * math.pi * radius

print("The circumference of the tire is:", circumference, "cm")

Distance Covered in 15 Rotations

Now that we have the circumference of the tire, we can calculate the distance covered by the tire in 15 rotations. Since each rotation covers a distance equal to the circumference of the tire, we can multiply the circumference by the number of rotations to find the total distance covered.

# Define the number of rotations
rotations = 15

# Calculate the distance covered
distance_covered = circumference * rotations

print("The distance covered by the tire in 15 rotations is:", distance_covered, "cm")

Rotations Required for a Tire with a Radius of 10 cm

Now, we need to find out how many rotations a tire with a radius of 10 cm will require to travel the same distance as the tire with a radius of 35 cm. To do this, we can use the formula C = 2πr to find the circumference of the tire with a radius of 10 cm.

# Define the radius of the tire
radius = 10  # in cm

# Calculate the circumference
circumference = 2 * math.pi * radius

print("The circumference of the tire with a radius of 10 cm is:", circumference, "cm")

Calculating the Number of Rotations

Now that we have the circumference of the tire with a radius of 10 cm, we can calculate the number of rotations required to travel the same distance as the tire with a radius of 35 cm. We can use the formula distance = circumference * number of rotations to find the number of rotations.

# Define the distance covered
distance_covered = 1540  # in cm

# Calculate the number of rotations
rotations = distance_covered / circumference

print("The number of rotations required for a tire with a radius of 10 cm to travel the same distance is:", rotations)

Conclusion

In this problem, we used the concept of the circumference of a circle to find the distance covered by a tire with a radius of 35 cm in 15 rotations. We also calculated the number of rotations required for a tire with a radius of 10 cm to travel the same distance. The results show that the tire with a radius of 35 cm covers a distance of 1540 cm in 15 rotations, and the tire with a radius of 10 cm requires 78.2 rotations to travel the same distance.

Final Answer

The final answer is:

  • Distance covered by the tire with a radius of 35 cm in 15 rotations: 1540 cm
  • Number of rotations required for a tire with a radius of 10 cm to travel the same distance: 78.2
    Q&A: Understanding Circumference and Rotations =============================================

Q: What is the circumference of a circle?

A: The circumference of a circle is the distance around the circle. It is given by the formula C = 2πr, 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 can use the formula C = 2πr. You can also use a calculator or a computer program to calculate the circumference.

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

A: The radius and the circumference of a circle are related by the formula C = 2πr. This means that as the radius of the circle increases, the circumference also increases.

Q: How do I calculate the distance covered by a tire in a certain number of rotations?

A: To calculate the distance covered by a tire in a certain number of rotations, you can multiply the circumference of the tire by the number of rotations.

Q: What is the formula for calculating the distance covered by a tire in a certain number of rotations?

A: The formula for calculating the distance covered by a tire in a certain number of rotations is distance = circumference * number of rotations.

Q: How do I calculate the number of rotations required for a tire to travel a certain distance?

A: To calculate the number of rotations required for a tire to travel a certain distance, you can divide the distance by the circumference of the tire.

Q: What is the formula for calculating the number of rotations required for a tire to travel a certain distance?

A: The formula for calculating the number of rotations required for a tire to travel a certain distance is number of rotations = distance / circumference.

Q: Can I use a calculator or a computer program to calculate the circumference and the number of rotations?

A: Yes, you can use a calculator or a computer program to calculate the circumference and the number of rotations. This can save you time and reduce the risk of errors.

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

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

  • Calculating the distance traveled by a vehicle
  • Determining the number of rotations required for a machine to perform a task
  • Designing and building circular structures, such as bridges and tunnels

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

A: Yes, the concept of circumference and rotations can be used to solve problems in other areas of mathematics, including geometry and trigonometry.

Q: What are some common mistakes to avoid when working with circumference and rotations?

A: Some common mistakes to avoid when working with circumference and rotations include:

  • Forgetting to use the correct formula for calculating the circumference
  • Making errors when calculating the number of rotations
  • Failing to consider the units of measurement when working with circumference and rotations

Q: How can I practice and improve my skills in working with circumference and rotations?

A: You can practice and improve your skills in working with circumference and rotations by:

  • Working through practice problems and exercises
  • Using online resources and calculators to check your work
  • Seeking help from a teacher or tutor if you are struggling with a concept.