A Drink Cooler Has The Shape Of A Rectangular Prism. It Has A Volume Of 1218 Cubic Inches. If It Has A Length Of $14 \frac{1}{2}$ Inches And A Width Of $10 \frac{1}{2}$ Inches, Then What Is The Height, In Inches, Of This

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A Drink Cooler's Secret: Uncovering the Height of a Rectangular Prism

When it comes to understanding the properties of three-dimensional objects, the concept of volume plays a crucial role. In this article, we will delve into the world of mathematics and explore the relationship between the volume, length, width, and height of a rectangular prism. Specifically, we will examine a drink cooler with a volume of 1218 cubic inches and dimensions of $14 \frac{1}{2}$ inches in length and $10 \frac{1}{2}$ inches in width. Our goal is to determine the height of this rectangular prism.

To find the height of the drink cooler, we need to use the formula for the volume of a rectangular prism, which is given by:

V = lwh

where V is the volume, l is the length, w is the width, and h is the height. In this case, we are given the volume (V = 1218 cubic inches), the length (l = $14 \frac{1}{2}$ inches), and the width (w = $10 \frac{1}{2}$ inches). We need to solve for the height (h).

Converting Mixed Numbers to Improper Fractions

Before we can plug in the values into the formula, we need to convert the mixed numbers to improper fractions. To do this, we multiply the whole number part by the denominator and add the numerator:

1412=(14×2)+12=28+12=29214 \frac{1}{2} = \frac{(14 \times 2) + 1}{2} = \frac{28 + 1}{2} = \frac{29}{2}

1012=(10×2)+12=20+12=21210 \frac{1}{2} = \frac{(10 \times 2) + 1}{2} = \frac{20 + 1}{2} = \frac{21}{2}

Now that we have converted the mixed numbers to improper fractions, we can plug in the values into the formula:

V = lwh 1218 = \frac{29}{2} \times \frac{21}{2} \times h

To solve for the height (h), we need to isolate h on one side of the equation. We can do this by multiplying both sides of the equation by the reciprocal of the product of the length and width:

h = \frac{1218}{\frac{29}{2} \times \frac{21}{2}}

To simplify the expression, we can multiply the fractions in the denominator:

h = \frac{1218}{\frac{29 \times 21}{2 \times 2}} h = \frac{1218}{\frac{609}{4}} h = \frac{1218 \times 4}{609}

Now we can simplify the expression by multiplying the numbers:

h = \frac{4872}{609}

To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 3:

h = \frac{1624}{203}

Converting the Fraction to a Decimal

To make the answer more readable, we can convert the fraction to a decimal by dividing the numerator by the denominator:

h ≈ 8.00

In this article, we used the formula for the volume of a rectangular prism to find the height of a drink cooler with a volume of 1218 cubic inches and dimensions of $14 \frac{1}{2}$ inches in length and $10 \frac{1}{2}$ inches in width. We converted the mixed numbers to improper fractions, plugged in the values into the formula, and solved for the height. The result is a height of approximately 8.00 inches.

Understanding the properties of three-dimensional objects is crucial in various real-world applications, such as:

  • Architecture: Architects use mathematical formulas to design buildings and structures that are safe and aesthetically pleasing.
  • Engineering: Engineers use mathematical formulas to design and develop new products and technologies.
  • Science: Scientists use mathematical formulas to understand and describe the natural world.

In conclusion, the concept of volume is a fundamental aspect of mathematics that has numerous real-world applications. By understanding the properties of three-dimensional objects, we can design and develop new products and technologies that improve our daily lives.
A Drink Cooler's Secret: Uncovering the Height of a Rectangular Prism (Q&A)

In our previous article, we explored the relationship between the volume, length, width, and height of a rectangular prism. We used the formula for the volume of a rectangular prism to find the height of a drink cooler with a volume of 1218 cubic inches and dimensions of $14 \frac{1}{2}$ inches in length and $10 \frac{1}{2}$ inches in width. In this article, we will answer some frequently asked questions about the concept of volume and rectangular prisms.

Q: What is the formula for the volume of a rectangular prism? A: The formula for the volume of a rectangular prism is V = lwh, where V is the volume, l is the length, w is the width, and h is the height.

Q: How do I convert a mixed number to an improper fraction? A: To convert a mixed number to an improper fraction, you multiply the whole number part by the denominator and add the numerator. For example, $14 \frac{1}{2} = \frac{(14 \times 2) + 1}{2} = \frac{28 + 1}{2} = \frac{29}{2}$

Q: How do I solve for the height of a rectangular prism? A: To solve for the height of a rectangular prism, you need to isolate h on one side of the equation. You can do this by multiplying both sides of the equation by the reciprocal of the product of the length and width.

Q: What is the height of the drink cooler with a volume of 1218 cubic inches and dimensions of $14 \frac{1}{2}$ inches in length and $10 \frac{1}{2}$ inches in width? A: The height of the drink cooler is approximately 8.00 inches.

Q: What are some real-world applications of the concept of volume? A: The concept of volume has numerous real-world applications, including architecture, engineering, and science. Architects use mathematical formulas to design buildings and structures that are safe and aesthetically pleasing. Engineers use mathematical formulas to design and develop new products and technologies. Scientists use mathematical formulas to understand and describe the natural world.

Q: Why is it important to understand the properties of three-dimensional objects? A: Understanding the properties of three-dimensional objects is crucial in various real-world applications. By understanding the properties of three-dimensional objects, we can design and develop new products and technologies that improve our daily lives.

Q: Can I use the formula for the volume of a rectangular prism to find the volume of other shapes? A: No, the formula for the volume of a rectangular prism only applies to rectangular prisms. If you need to find the volume of other shapes, you will need to use a different formula.

In conclusion, the concept of volume is a fundamental aspect of mathematics that has numerous real-world applications. By understanding the properties of three-dimensional objects, we can design and develop new products and technologies that improve our daily lives. We hope that this article has helped to answer some of your questions about the concept of volume and rectangular prisms.

  • Mathematics textbooks: If you are looking for more information on the concept of volume and rectangular prisms, you may want to consult a mathematics textbook.
  • Online resources: There are many online resources available that can help you learn more about the concept of volume and rectangular prisms.
  • Mathematics software: You can use mathematics software, such as Mathematica or Maple, to explore the concept of volume and rectangular prisms.

In conclusion, the concept of volume is a fundamental aspect of mathematics that has numerous real-world applications. By understanding the properties of three-dimensional objects, we can design and develop new products and technologies that improve our daily lives. We hope that this article has helped to answer some of your questions about the concept of volume and rectangular prisms.