Sprinkler Coverage: Calculating Circumference

Hey everyone! Ever wondered how far a sprinkler sprays and what shape it makes? Let's dive into a fun math problem about sprinklers, circles, and how to figure out the distance covered. Today, we'll tackle a problem about a sprinkler that sprays water in a circular pattern, and we'll calculate the circumference of that circle. Get ready to put on your math hats, because we're about to get started.

Understanding the Problem: The Sprinkler's Reach

Okay, so here's the deal: The sprinkler shoots water out, and that water goes in a circle. We're told that the water reaches out 21 feet from the sprinkler. This 21 feet is the radius of the circle, which is the distance from the center (where the sprinkler is) to any point on the edge of the circle. Now, what we want to find out is the circumference of that circle. The circumference is like the perimeter – the total distance around the outside of the circle.

So, let's break it down. Our main keyword is sprinkler spray coverage, which is exactly what we're trying to figure out. The sprinkler makes a perfect circle, and we have the radius (21 feet). To find the circumference, we need to use a formula, and we'll use the approximation of pi, which is 22/7, like the question says. This is how we can solve this math problem. We will learn how to calculate the circumference and what it represents in terms of the water spray. The sprinkler's reach of 21 feet is crucial because it defines the size of the circle. We'll see how the formula uses this reach to find the distance the water travels. This problem combines real-world understanding with basic geometric principles, making it a practical and engaging example of how math applies to everyday life. The circumference is a measure of how far the water extends from the sprinkler. We're going to find the distance around the outside of the circle created by the sprinkler.

Key Components

• Radius: The distance from the center of the circle to any point on its edge (21 feet in our case).
• Circumference: The total distance around the circle that the sprinkler sprays.
• Pi (π): A mathematical constant (approximately 3.14159), often approximated as 22/7 for calculations.

With these elements, let's figure out the circumference!

Calculating the Circumference: Step by Step

Alright, time to get down to business! The formula for the circumference of a circle is: Circumference = 2 * π * r, where 'r' is the radius and π (pi) is the number approximately equal to 22/7, as instructed. Let's plug in the numbers we know.

Step 1: Identify the given values.

• Radius (r) = 21 feet.
• π (pi) = 22/7.

Step 2: Apply the formula.

• Circumference = 2 * π * r
• Circumference = 2 * (22/7) * 21

Step 3: Solve the equation.

• First, multiply 2 by 22/7, which gives us 44/7.
• Next, multiply 44/7 by 21.
• (44/7) * 21 = (44 * 21) / 7 = 924/7
• 924/7 = 132

So, the circumference is 132 feet. This means the sprinkler sprays water around a circle with a total distance of 132 feet. This problem requires you to understand the relationships between the radius, diameter, and circumference of a circle. You will use these values to solve the problem effectively. The mathematical steps involve using the formula for calculating circumference, which is a fundamental concept in geometry. This includes substitution and performing arithmetic operations correctly to determine the final answer. We also applied the formula using the given values.

The whole process involves understanding the problem, identifying the given values, selecting the correct formula, and applying it step-by-step to find the final answer. By correctly applying the formula and performing the calculations accurately, we arrive at the circumference of the circle created by the sprinkler's spray.

Conclusion: The Sprinkler's Circular Reach

Awesome! We successfully found the circumference of the circle created by the sprinkler. The sprinkler sprays water in a circle with a circumference of 132 feet. This means if you were to walk along the outer edge of the water spray, you'd walk a total distance of 132 feet. We took a real-world problem and used a bit of math to solve it. And that's how we can use math to find how far the sprinkler sprays! Knowing the circumference helps in understanding the area covered by the sprinkler. This knowledge could be useful if you were planning a garden or wanted to know how much of your lawn gets watered. The calculation underscores the practical application of mathematical concepts in daily situations. This shows how fundamental mathematical formulas can be used to understand and solve real-world problems. This helps in solving geometric problems involving circles in different scenarios.

Final Answer:

The circumference of the circle sprayed by the sprinkler is 132 feet. I hope this explanation was helpful. Keep practicing, and you'll get better at these types of problems!