4.07 Quiz: Finding The Volume Of A PrismA Rectangular Prism Has A Length Of 3 1 2 3 \frac{1}{2} 3 2 1 ​ Inches, A Width Of 5 Inches, And A Height Of 1 1 2 1 \frac{1}{2} 1 2 1 ​ Inches. What Is The Volume Of The Prism?Enter Your Answer In The Box As A

Understanding the Concept of Volume

In mathematics, the volume of a three-dimensional object is a measure of the amount of space inside the object. For a rectangular prism, the volume can be calculated using the formula: V = lwh, where V is the volume, l is the length, w is the width, and h is the height.

Calculating the Volume of a Rectangular Prism

To find the volume of a rectangular prism, we need to multiply the length, width, and height of the prism. Let's use the given dimensions: a length of $3 \frac{1}{2}$ inches, a width of 5 inches, and a height of $1 \frac{1}{2}$ inches.

Converting Mixed Numbers to Improper Fractions

Before we can multiply the dimensions, we need to convert the mixed numbers to improper fractions. To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and add the numerator.

• $3 \frac{1}{2} = \frac{(3 \times 2) + 1}{2} = \frac{7}{2}$
• $1 \frac{1}{2} = \frac{(1 \times 2) + 1}{2} = \frac{3}{2}$

Multiplying the Dimensions

Now that we have the dimensions in improper fractions, we can multiply them to find the volume.

• V = lwh = (7/2) × 5 × (3/2)

To multiply fractions, we multiply the numerators and denominators separately.

• V = (7 × 5 × 3) / (2 × 2)
• V = 105 / 4

Simplifying the Fraction

To simplify the fraction, we can divide the numerator and denominator by their greatest common divisor (GCD). The GCD of 105 and 4 is 1, so the fraction is already simplified.

• V = 105 / 4

Converting the Fraction to a Decimal

To make the answer more readable, we can convert the fraction to a decimal.

• V = 105 / 4 = 26.25

Conclusion

The volume of the rectangular prism is 26.25 cubic inches.

Real-World Applications of Volume

Understanding the concept of volume is essential in various real-world applications, such as:

• Architecture: Architects use volume calculations to design buildings and ensure that they have enough space for occupants.
• Engineering: Engineers use volume calculations to design systems, such as pipes and tanks, that can hold a certain amount of fluid.
• Science: Scientists use volume calculations to measure the amount of substance in a container.

Common Mistakes to Avoid

When calculating the volume of a rectangular prism, it's essential to avoid common mistakes, such as:

• Incorrectly converting mixed numbers to improper fractions
• Multiplying the dimensions incorrectly
• Not simplifying the fraction

Practice Problems

To practice finding the volume of a rectangular prism, try the following problems:

• A rectangular prism has a length of 4 inches, a width of 6 inches, and a height of 2 inches. What is the volume of the prism?
• A rectangular prism has a length of 3 inches, a width of 5 inches, and a height of 1 inch. What is the volume of the prism?

Conclusion

Q: What is the formula for finding the volume of a rectangular prism?

A: The formula for finding 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 by the denominator and add the numerator. For example, to convert $3 \frac{1}{2}$ to an improper fraction, you would multiply 3 by 2 and add 1, resulting in $\frac{7}{2}$.

Q: What is the difference between a mixed number and an improper fraction?

A: A mixed number is a combination of a whole number and a fraction, while an improper fraction is a fraction where the numerator is greater than the denominator. For example, $3 \frac{1}{2}$ is a mixed number, while $\frac{7}{2}$ is an improper fraction.

Q: How do I multiply fractions?

A: To multiply fractions, you multiply the numerators and denominators separately. For example, to multiply $\frac{2}{3}$ and $\frac{3}{4}$, you would multiply 2 and 3 to get 6, and multiply 3 and 4 to get 12, resulting in $\frac{6}{12}$, which can be simplified to $\frac{1}{2}$.

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) is the largest number that divides two or more numbers without leaving a remainder. For example, the GCD of 12 and 18 is 6, because 6 is the largest number that divides both 12 and 18 without leaving a remainder.

Q: How do I simplify a fraction?

A: To simplify a fraction, you divide the numerator and denominator by their greatest common divisor (GCD). For example, to simplify $\frac{12}{18}$, you would divide both 12 and 18 by 6, resulting in $\frac{2}{3}$.

Q: What is the difference between a decimal and a fraction?

A: A decimal is a way of representing a number using a point to separate the whole number part from the fractional part, while a fraction is a way of representing a number as a ratio of two integers. For example, 0.5 is a decimal, while $\frac{1}{2}$ is a fraction.

Q: How do I convert a fraction to a decimal?

A: To convert a fraction to a decimal, you divide the numerator by the denominator. For example, to convert $\frac{1}{2}$ to a decimal, you would divide 1 by 2, resulting in 0.5.

Q: What are some real-world applications of volume?

A: Some real-world applications of volume include:

• Architecture: Architects use volume calculations to design buildings and ensure that they have enough space for occupants.
• Engineering: Engineers use volume calculations to design systems, such as pipes and tanks, that can hold a certain amount of fluid.
• Science: Scientists use volume calculations to measure the amount of substance in a container.

Q: What are some common mistakes to avoid when finding the volume of a prism?

A: Some common mistakes to avoid when finding the volume of a prism include:

• Incorrectly converting mixed numbers to improper fractions
• Multiplying the dimensions incorrectly
• Not simplifying the fraction

Q: How can I practice finding the volume of a prism?

A: You can practice finding the volume of a prism by trying the following problems:

• A rectangular prism has a length of 4 inches, a width of 6 inches, and a height of 2 inches. What is the volume of the prism?
• A rectangular prism has a length of 3 inches, a width of 5 inches, and a height of 1 inch. What is the volume of the prism?