The length L(r) of a wire to fence a circular garden is the product of 2 pi and it's radius r

To find the length \( L(r) \) of a wire needed to fence a circular garden, given that \( L(r) \) is the product of \( 2\pi \) and the radius \( r \), we can use the formula for the circumference of a circle.

The formula for the circumference \( C \) of a circle is:

\[ C = 2\pi r \]

Here, \( C \) represents the length \( L(r) \) of the wire needed to fence the garden. Therefore, the length \( L(r) \) can be expressed as:

\[ L(r) = 2\pi r \]

This equation tells us that the length of the wire is directly proportional to the radius of the circular garden.

Would you like a detailed explanation of how this formula is derived, or do you have any questions?

Here are some related questions to further explore this topic:

1. How does the length of the wire change if the radius is doubled?
2. What would be the length of the wire needed for a circular garden with a radius of 5 meters?
3. How is the formula for the circumference of a circle derived?
4. If the radius of a circular garden is increased by 1 meter, by how much does the length of the wire increase?
5. Can you calculate the length of the wire needed for a circular garden with a radius of 10 meters?
6. How would you find the radius of a circular garden if you know the length of the wire?
7. What is the significance of the constant \( \pi \) in the formula for the circumference of a circle?
8. How would the formula change if you were fencing an elliptical garden instead?

**Tip:** Remember that \( \pi \) (pi) is an irrational number approximately equal to 3.14159, and it plays a crucial role in calculations involving circles and circular objects.

Learn how to calculate the length of wire needed to fence a circular garden using the formula L(r) = 2\pi r. Understand the relationship between the length of the wire and the radius of the garden. Suitable for Grades 6-8 students.

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