Calculating the Volume of the Fish Tank

Oct 13, 2025 by miodeya.com 113 views

Understanding the Problem

A fish tank is a cube with a side length of $$4 \frac{1}{2}$$ feet. To determine the volume of water needed to completely fill the fish tank, we need to calculate the volume of the cube. The volume of a cube is given by the formula: V = s^3, where s is the length of a side of the cube.

Calculating the Volume of the Fish Tank

To calculate the volume of the fish tank, we need to cube the length of a side. The length of a side is given as $$4 \frac1}{2}$$ feet. We can convert this mixed number to an improper fraction $$4 \frac{1{2} = \frac{9}{2}$$ feet.

Now, we can cube the length of a side: $$\left(\frac{9}{2}\right)^3 = \frac{729}{8}$$ cubic feet.

Simplifying the Answer

To simplify the answer, we can convert the improper fraction to a mixed number: $$\frac{729}{8} = 91 \frac{1}{8}$$ cubic feet.

Conclusion

The volume of water needed to completely fill the fish tank is $$91 \frac{1}{8}$$ cubic feet.

Calculating the Volume of a Cube: A Step-by-Step Guide

Step 1: Understand the Problem

To calculate the volume of a cube, we need to understand the formula: V = s^3, where s is the length of a side of the cube.

Step 2: Convert the Length of a Side to an Improper Fraction

If the length of a side is given as a mixed number, we need to convert it to an improper fraction. For example, $$4 \frac{1}{2} = \frac{9}{2}$$ feet.

Step 3: Cube the Length of a Side

To calculate the volume of the cube, we need to cube the length of a side. For example, $$\left(\frac{9}{2}\right)^3 = \frac{729}{8}$$ cubic feet.

Step 4: Simplify the Answer

To simplify the answer, we can convert the improper fraction to a mixed number. For example, $$\frac{729}{8} = 91 \frac{1}{8}$$ cubic feet.

Step 5: Write the Final Answer

The final answer is the volume of the cube, which is $$91 \frac{1}{8}$$ cubic feet.

Common Mistakes to Avoid

Not converting the length of a side to an improper fraction: If the length of a side is given as a mixed number, we need to convert it to an improper fraction before cubing it.
Not cubing the length of a side: To calculate the volume of the cube, we need to cube the length of a side.
Not simplifying the answer: To simplify the answer, we can convert the improper fraction to a mixed number.

Real-World Applications

Calculating the volume of a cube has many real-world applications, such as:

Designing fish tanks: To determine the volume of water needed to completely fill a fish tank, we need to calculate the volume of the cube.
Building construction: To calculate the volume of a building, we need to calculate the volume of the cube.
Engineering: To calculate the volume of a complex shape, we need to break it down into smaller cubes and calculate the volume of each cube.

Conclusion

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

A: The formula for calculating the volume of a cube is V = s^3, where s is the length of a side of the cube.

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

A: To convert a mixed number to an improper fraction, you need to multiply the whole number by the denominator and add the numerator. For example, $$4 \frac{1}{2} = \frac{(4 \times 2) + 1}{2} = \frac{9}{2}$$.

Q: How do I cube a fraction?

A: To cube a fraction, you need to cube the numerator and the denominator separately. For example, $$\left(\frac{9}{2}\right)^3 = \frac{729}{8}$$.

Q: How do I simplify an improper fraction?

A: To simplify an improper fraction, you need to divide the numerator by the denominator. For example, $$\frac{729}{8} = 91 \frac{1}{8}$$.

Q: What are some real-world applications of calculating the volume of a cube?

A: Calculating the volume of a cube has many real-world applications, such as designing fish tanks, building construction, and engineering.

Q: What are some common mistakes to avoid when calculating the volume of a cube?

A: Some common mistakes to avoid when calculating the volume of a cube include not converting the length of a side to an improper fraction, not cubing the length of a side, and not simplifying the answer.

Q: How do I calculate the volume of a cube with a side length of 5 feet?

A: To calculate the volume of a cube with a side length of 5 feet, you need to cube the length of a side: $$5^3 = 125$$ cubic feet.

Q: How do I calculate the volume of a cube with a side length of 3 feet 1 inch?

A: To calculate the volume of a cube with a side length of 3 feet 1 inch, you need to convert the length of a side to an improper fraction: $$3 \frac1}{12} = \frac{37}{12}$$ feet. Then, you need to cube the length of a side $$\left(\frac{37{12}\right)^3 = \frac{2197}{1728}$$ cubic feet.

Q: How do I calculate the volume of a cube with a side length of 2 feet 5 inches?

A: To calculate the volume of a cube with a side length of 2 feet 5 inches, you need to convert the length of a side to an improper fraction: $$2 \frac5}{12} = \frac{29}{12}$$ feet. Then, you need to cube the length of a side $$\left(\frac{29{12}\right)^3 = \frac{24389}{1728}$$ cubic feet.

Conclusion

Calculating the volume of a cube is a simple yet important concept in mathematics. By following the steps outlined in this article and avoiding common mistakes, you can calculate the volume of a cube and apply it to real-world problems.