Mastering the TEAS ATI Mathematics Test: Unraveling Box Volume Problems

A box has a square base of 5 feet in length, a width of 5 feet, and a height of h feet. If the volume of the rectangular solid is 200 cubic feet, which equation may be used to find h?

• A. 5h = 200
• B. 5h² = 200
• C. 25h = 200
• D. h = 200 ÷ 5

Answer: (C)

To determine the correct equation to find the height \( h \) of the box, we start with the formula for the volume of a rectangular solid, which is given by: \[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \] In this scenario, the dimensions of the box are defined as follows: the length is 5 feet, the width is also 5 feet, and the height is \( h \) feet. Plugging in these values into the volume formula gives us: \[ \text{Volume} = 5 \times 5 \times h \] This simplifies to: \[ \text{Volume} = 25h \] Since we know the volume of the box is 200 cubic feet, we set the equation equal to 200: \[ 25h = 200 \] This equation, \( 25h = 200 \), allows us to isolate \( h \) by dividing both sides by 25, which leads us to finding the height of the box. This is why the equation \( 25h = 200 \) is suitable for finding \( h \) in this

When it comes to the TEAS ATI Mathematics Test, the quest for mastering box volume problems holds a pivotal place. Imagine standing before a fascinating puzzle: a box with a square base measuring 5 feet by 5 feet and an unknown height, ( h ). Just how do you figure out that elusive height if you know the volume is 200 cubic feet? That's where understanding your formulas plays a crucial role.

Let’s break it down together, shall we? The formula for the volume of a rectangular solid is pretty straightforward:

[

\text{Volume} = \text{length} \times \text{width} \times \text{height}

]

In this example, you’ve got a solid with dimensions that boils down to the following: 5 feet for both length and width, and h feet for height. Plugging those figures into the volume formula gives us:

[

\text{Volume} = 5 \times 5 \times h

]

Simplifying that, you get:

[

\text{Volume} = 25h

]

So now we’ve captured a crucial piece of the puzzle! With the knowledge that the volume equals 200 cubic feet, we can set up the equation:

[

25h = 200

]

Isn’t it satisfying when everything clicks into place? Now, if you want to find height, ( h ), you can simply divide both sides of the equation by 25, leading you to:

[

h = \frac{200}{25} = 8

]

Now, let’s pause for a moment. Why is understanding this specific problem important? Well, not only does it sharpen your analytical skills, but it also builds confidence when facing similar questions that can pop up during your exam. It’s like training for a race; the more you practice, the more comfortable you become on the day of the big event.

You might be thinking, "What if the numbers were different—like different measurements, or perhaps a box shape that isn’t rectangular?" That’s the beauty of math; it adapts and flows with the rules. Familiarizing yourself with various box problems can enhance your overall problem-solving toolkit.

But let’s keep it centered around our 5-foot box for a moment. Establishing that ( 25h = 200 ) isn’t just about finding height; it’s about grasping the underlying concepts of volume and how they interconnect. It brings to the forefront an essential mathematical principle—one that will serve you time and again.

Ultimately, whether you encounter straightforward questions about box volume or more complex ones, mastering these foundational concepts can significantly impact your overall performance on the TEAS ATI Mathematics Test. So the next time you come across a similar problem, reflect back on this experience. It’s not merely about finding the answer but embracing the journey of learning that goes with it!