The fence around a circular pool is 75 ft long. This intriguing mathematical problem invites us to explore the relationship between the circumference of a circle and the length of its enclosing fence, ultimately leading us to determine the radius of the pool.
Embark on this journey of discovery as we unravel the intricacies of this captivating puzzle.
The circumference of a circle, a fundamental concept in geometry, is the distance around its outer edge. It is directly proportional to the radius of the circle, with a larger radius resulting in a greater circumference. Understanding this relationship is crucial for solving our problem.
Circumference of Circular Pool: The Fence Around A Circular Pool Is 75 Ft Long.
The circumference of a circle is the distance around the circle’s edge. It is calculated using the formula:
Circumference = 2πr
where π (pi) is a mathematical constant approximately equal to 3.14 and r is the radius of the circle.
For example, if a circle has a radius of 5 feet, its circumference would be:
Circumference = 2π(5) = 10π feet ≈ 31.4 feet
Relationship between Circumference and Fence Length
The length of the fence around a circular pool is equal to the circumference of the pool.
This is because the fence must enclose the entire pool, and the distance around the pool’s edge is the same as the distance around the fence.
Solving for Pool Radius
To solve for the radius of a circular pool given the fence length, we can use the formula for circumference and set it equal to the fence length:
Fence length = 2πr
Solving for r, we get:
r = Fence length / 2π
For example, if the fence around a circular pool is 75 feet long, the radius of the pool would be:
r = 75 ft / 2π ≈ 11.94 feet
Illustrating the Solution, The fence around a circular pool is 75 ft long.
| Fence Length | Pool Radius | Circumference |
|---|---|---|
| 75 feet | 11.94 feet | 75 feet |
This table shows the relationship between the fence length, pool radius, and circumference of a circular pool.
FAQ Overview
What is the formula for calculating the circumference of a circle?
Circumference = 2πr, where r is the radius of the circle.
How do I find the radius of a circle if I know the circumference?
Radius = Circumference / 2π.
