Calculating the Length of a Red Stripe on a Water Tank

Jaime must paint a 16" wide, red stripe completely around a water tank at a centered height of 18 feet. The tank's dimensions are 25 feet high and 150 feet in diameter. How long, in linear feet, will the stripe be?

• A. 300 feet
• B. 471 feet
• C. 470 feet
• D. 440 feet

Answer: (B)

To determine the length of the stripe that Jaime needs to paint around the water tank, it is essential to calculate the circumference of the tank. The tank is in the shape of a cylinder, and the formula for the circumference (C) of a cylinder is given by the formula: C = π * d where "d" is the diameter of the cylinder. In this case, the diameter of the water tank is provided as 150 feet. To find the circumference: C = π * 150 feet Using the approximate value of π (3.14) for calculations: C = 3.14 * 150 feet ≈ 471 feet Thus, the length of the red stripe that Jaime must paint completely around the tank at the specified height of 18 feet is approximately 471 linear feet. This makes the option stating 471 feet the correct answer, as it accurately represents the circumference found using the standard geometric formula for a cylinder. The correct answer aligns with the calculation of the tank's circumference, solidifying the understanding of how to measure the perimeter of cylindrical objects accurately.

Calculating the Length of a Stripe: A Fun Dive into Geometry

Have you ever found yourself knee-deep in a DIY project, paintbrush in hand, staring at an object trying to figure out how much paint you need? Whether you're on your home improvement mission or just curious about math in everyday life, it often comes down to understanding some basic geometry. Let’s jump into a scenario involving Jaime, a determined individual who must paint a bold red stripe around a cylindrical water tank. But, before opening that can of paint, there’s math to be tackled!

What's the Challenge?

Jaime’s task is to paint a 16-inch wide stripe at a height of 18 feet around a water tank that stands a towering 25 feet high and is a hefty 150 feet in diameter. Sounds straightforward, right? But how do you figure out the length of that stripe? You’ve got to remember your geometry basics!

Understanding the Geometry

First, we need to determine the circumference of the tank. You see, a water tank isn’t just a container; it’s shaped like a cylinder. And what better way to understand a cylinder than by remembering that iconic formula for circumference? Drumroll, please:

[ C = π \times d ]

where “d” is the diameter of the cylinder. In this case, Jaime knows the tank’s diameter is 150 feet.

So, let’s break that down.

Time for Some Calculations

We already have our diameter. Now it’s time to put it into that formula.

[ C = π \times 150 ]

For easier calculations, we can use π as approximately 3.14. That gives us:

[ C = 3.14 \times 150 ]

Cha-ching! When you multiply that out, you get about:

[ C ≈ 471 \text{ feet} ]

So voilà! The red stripe Jaime must paint around the tank measures approximately 471 linear feet. Isn’t it fascinating how a simple mathematical principle can play a crucial role in something as hands-on as painting?

Why Does This Matter?

Now, you might be thinking, "Why should I care about calculating the length of that stripe?” Well, here’s where it connects to real life. Being able to calculate the needed materials (whether paint, tiles, or fabric) helps avoid wastage and ensures your project runs smoothly. No one wants to be caught midway through a project, realizing they've bought too little or too much of something!

Also, think about it: This calculation is like a miniature version of planning how to tackle bigger challenges in life or work. Knowing how to measure, plan, and execute—skills tied to this calculation—are incredibly valuable. So, whether you're painting a tank or assembling furniture, it's all about knowing where you stand (literally and figuratively)!

A Quick Recap

To wrap things up, Jaime's journey around that tank teaches us a few lessons:

1. Cylindrical Shapes Rule: Always remember that when working with cylindrical objects, the formula for circumference is your best friend.

2. Precision Matters: Getting your measurements right means you won’t need to make extra trips to the hardware store, which can save both time and money.

3. Math Isn’t Just for Class: Understanding these concepts can simplify real-world tasks and make you feel like a total pro while tackling home improvement projects.

Every time you pick up a task that requires measurements or calculations, remember Jaime’s stripe. Not only will it make you smile, but it’ll also prep you for whatever geometry-related challenge heads your way next.

Final Thoughts

The next time you find yourself facing a similar home project, whether it’s painting, landscaping, or even setting up a tent, consider how geometry applies to your task. A little bit of math can go a long way in ensuring your ambitions take shape—literally! Happy painting, measuring, and creating!