What Is The Volume Of A Rectangular Prism With A Length Of 12 1 4 12 \frac{1}{4} 12 4 1 ​ Yards, A Width Of 6 Yards, And A Height Of 7 Yards?A. 257 1 4 Yd 3 257 \frac{1}{4} \, \text{yd}^3 257 4 1 ​ Yd 3 B. 402 1 2 Yd 3 402 \frac{1}{2} \, \text{yd}^3 402 2 1 ​ Yd 3 C. $514 \frac{1}{2}

Understanding the Concept of Volume

In mathematics, the volume of a rectangular prism is a fundamental concept that is used to calculate the amount of space inside a three-dimensional object. A rectangular prism is a three-dimensional shape with six rectangular faces, and its volume is calculated by multiplying the length, width, and height of the prism.

Calculating the Volume of a Rectangular Prism

To calculate the volume of a rectangular prism, we need to multiply the length, width, and height of the prism. The formula for calculating the volume of a rectangular prism is:

Volume = Length × Width × Height

Given Values

In this problem, we are given the following values:

• Length: $12 \frac{1}{4}$ yards
• Width: 6 yards
• Height: 7 yards

Converting Mixed Numbers to Improper Fractions

Before we can calculate the volume, we need to convert the mixed number $12 \frac{1}{4}$ to an improper fraction. To do this, we multiply the whole number part (12) by the denominator (4), and then add the numerator (1). This gives us:

$12 \frac{1}{4} = \frac{(12 \times 4) + 1}{4} = \frac{48 + 1}{4} = \frac{49}{4}$

Calculating the Volume

Now that we have converted the mixed number to an improper fraction, we can calculate the volume of the rectangular prism. We multiply the length, width, and height of the prism:

Volume = Length × Width × Height = $\frac{49}{4} \times 6 \times 7$ = $\frac{49 \times 6 \times 7}{4}$ = $\frac{2458}{4}$ = $617 \frac{1}{4}$

However, this is not one of the answer choices. Let's try another approach.

Multiplying the Numerator and Denominator

Another way to calculate the volume is to multiply the numerator and denominator of the improper fraction, and then multiply the result by the width and height of the prism:

Volume = Length × Width × Height = $\frac{49}{4} \times 6 \times 7$ = $\frac{49 \times 6 \times 7}{4}$ = $\frac{49 \times 42}{4}$ = $\frac{2058}{4}$ = $514 \frac{1}{2}$

Conclusion

In conclusion, the volume of a rectangular prism with a length of $12 \frac{1}{4}$ yards, a width of 6 yards, and a height of 7 yards is $514 \frac{1}{2} \, \text{yd}^3$. This is the correct answer choice.

References

• [1] "Volume of a Rectangular Prism." Math Open Reference, mathopenref.com/rectangularprism.html.
• [2] "Rectangular Prism." Wikipedia, en.wikipedia.org/wiki/Rectangular_prism.

Frequently Asked Questions

• Q: What is the formula for calculating the volume of a rectangular prism? A: The formula for calculating the volume of a rectangular prism is: Volume = Length × Width × Height.
• Q: How do I convert a mixed number to an improper fraction? A: To convert a mixed number to an improper fraction, multiply the whole number part by the denominator, and then add the numerator.
• Q: What is the volume of a rectangular prism with a length of $12 \frac{1}{4}$ yards, a width of 6 yards, and a height of 7 yards? A: The volume of a rectangular prism with a length of $12 \frac{1}{4}$ yards, a width of 6 yards, and a height of 7 yards is $514 \frac{1}{2} \, \text{yd}^3$.
  Frequently Asked Questions (FAQs) About Rectangular Prisms ================================================================

Q: What is a rectangular prism?

A: A rectangular prism is a three-dimensional shape with six rectangular faces. It has a length, width, and height, and its volume is calculated by multiplying these three dimensions.

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

A: The formula for calculating the volume of a rectangular prism is: Volume = Length × Width × Height.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, multiply the whole number part by the denominator, and then add the numerator. For example, to convert $12 \frac{1}{4}$ to an improper fraction, you would multiply 12 by 4 and add 1, giving you $\frac{49}{4}$.

Q: What is the volume of a rectangular prism with a length of $12 \frac{1}{4}$ yards, a width of 6 yards, and a height of 7 yards?

A: The volume of a rectangular prism with a length of $12 \frac{1}{4}$ yards, a width of 6 yards, and a height of 7 yards is $514 \frac{1}{2} \, \text{yd}^3$.

Q: How do I calculate the volume of a rectangular prism with decimal dimensions?

A: To calculate the volume of a rectangular prism with decimal dimensions, simply multiply the length, width, and height of the prism. For example, if the length is 4.5 yards, the width is 2.8 yards, and the height is 3.2 yards, the volume would be:

Volume = Length × Width × Height = 4.5 × 2.8 × 3.2 = 40.32

Q: Can I use a calculator to calculate the volume of a rectangular prism?

A: Yes, you can use a calculator to calculate the volume of a rectangular prism. Simply enter the length, width, and height of the prism into the calculator, and it will give you the volume.

Q: What is the difference between a rectangular prism and a cube?

A: A rectangular prism is a three-dimensional shape with six rectangular faces, while a cube is a three-dimensional shape with six square faces. The main difference between the two is that a cube has equal length, width, and height, while a rectangular prism does not.

Q: How do I find the surface area of a rectangular prism?

A: To find the surface area of a rectangular prism, you need to calculate the area of each of the six faces and add them together. The formula for the surface area of a rectangular prism is:

Surface Area = 2 × (Length × Width + Width × Height + Height × Length)

Q: Can I use a formula to calculate the surface area of a rectangular prism?

A: Yes, you can use a formula to calculate the surface area of a rectangular prism. The formula is:

Surface Area = 2 × (Length × Width + Width × Height + Height × Length)

Q: What is the volume of a rectangular prism with a length of 5 yards, a width of 3 yards, and a height of 2 yards?

A: The volume of a rectangular prism with a length of 5 yards, a width of 3 yards, and a height of 2 yards is:

Volume = Length × Width × Height = 5 × 3 × 2 = 30

Q: How do I calculate the volume of a rectangular prism with fractional dimensions?

A: To calculate the volume of a rectangular prism with fractional dimensions, simply multiply the length, width, and height of the prism. For example, if the length is $\frac{1}{2}$ yards, the width is $\frac{3}{4}$ yards, and the height is $\frac{2}{3}$ yards, the volume would be:

Volume = Length × Width × Height = $\frac{1}{2} \times \frac{3}{4} \times \frac{2}{3}$ = $\frac{1}{4}$