Recalling the Formula for the Volume of a Cube

Oct 13, 2025 by talynt.org 49 views

Introduction

In geometry, a cube is a three-dimensional solid object with six square faces, each of which is a square. The volume of a cube is a crucial property that can be used to determine the length of its sides. In this article, we will explore the relationship between the volume of a cube and the length of its sides, and we will derive an expression to represent the length of a side of the cube.

Recalling the Formula for the Volume of a Cube

The formula for the volume of a cube is given by:

V = s^3

where $V$ is the volume of the cube and $s$ is the length of a side of the cube. This formula is derived from the fact that the volume of a cube is equal to the product of the lengths of its three sides.

Given Information

We are given that the volume of the cube is 27 cubic inches. We can use this information to find the length of a side of the cube.

Deriving the Expression for the Length of a Side

To find the length of a side of the cube, we can rearrange the formula for the volume of a cube to isolate $s$ . We can do this by taking the cube root of both sides of the equation:

s^3 = V

s = \sqrt[3]{V}

Substituting the given value of $V$ into this equation, we get:

s = \sqrt[3]{27}

Evaluating the Expression

To evaluate the expression $\sqrt[3]{27}$ , we can use the fact that $27 = 3^3$ . Therefore, we can rewrite the expression as:

s = \sqrt[3]{3^3}

Using the property of radicals that $\sqrt[n]{a^n} = a$ , we can simplify the expression to:

s = 3

Conclusion

In this article, we have derived an expression to represent the length of a side of a cube, given its volume. We have shown that the length of a side of a cube is equal to the cube root of its volume. We have also evaluated the expression $\sqrt[3]{27}$ to find that the length of a side of the cube is 3 inches.

Discussion

The expression $\sqrt[3]{27}$ represents the length of a side of a cube with a volume of 27 cubic inches. This expression can be used to find the length of a side of a cube, given its volume. The cube root of 27 is equal to 3, which means that the length of a side of a cube with a volume of 27 cubic inches is 3 inches.

Answer

The correct answer is:

A. $s = \sqrt[3]{27}$

Additional Information

The formula for the volume of a cube is $V = s^3$ , where $V$ is the volume of the cube and $s$ is the length of a side of the cube. This formula can be used to find the length of a side of a cube, given its volume.

Example

Suppose we have a cube with a volume of 64 cubic inches. We can use the formula for the volume of a cube to find the length of a side of the cube:

V = s^3

64 = s^3

s = \sqrt[3]{64}

s = 4

Therefore, the length of a side of the cube is 4 inches.

Conclusion

$In this article, we have explored the relationship between the volume of a cube and the length of its sides. We have derived an expression to represent the length of a side of a cube, given its volume, and we have evaluated the expression $\sqrt[3]{27}$ to find that the length of a side of the cube is 3 inches. We have also provided an example of how to use the formula for the volume of a cube to find the length of a side of a cube.<br/> **The Volume of a Cube: Q&A**$

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

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

Q: How do I find the length of a side of a cube, given its volume?

A: To find the length of a side of a cube, given its volume, you can use the formula $s = \sqrt[3]{V}$ , where $V$ is the volume of the cube.

Q: What is the relationship between the volume of a cube and the length of its sides?

A: The volume of a cube is equal to the product of the lengths of its three sides. This can be expressed mathematically as $V = s^3$ , where $V$ is the volume of the cube and $s$ is the length of a side of the cube.

Q: Can I use the formula for the volume of a cube to find the length of a side of a cube with a volume of 125 cubic inches?

A: Yes, you can use the formula $s = \sqrt[3]{V}$ to find the length of a side of a cube with a volume of 125 cubic inches. Plugging in the value of $V$ , we get:

s = \sqrt[3]{125}

s = 5

Therefore, the length of a side of the cube is 5 inches.

Q: What is the cube root of 216?

A: The cube root of 216 is 6, since $6^3 = 216$ .

Q: Can I use the formula for the volume of a cube to find the length of a side of a cube with a volume of 729 cubic inches?

A: Yes, you can use the formula $s = \sqrt[3]{V}$ to find the length of a side of a cube with a volume of 729 cubic inches. Plugging in the value of $V$ , we get:

s = \sqrt[3]{729}

s = 9

Therefore, the length of a side of the cube is 9 inches.

Q: What is the relationship between the cube root and the exponentiation operation?

A: The cube root operation is the inverse of the exponentiation operation with a base of 3. In other words, $\sqrt[3]{a} = b$ is equivalent to $b^3 = a$ .

Q: Can I use the formula for the volume of a cube to find the length of a side of a cube with a volume of 1000 cubic inches?

A: Yes, you can use the formula $s = \sqrt[3]{V}$ to find the length of a side of a cube with a volume of 1000 cubic inches. Plugging in the value of $V$ , we get:

s = \sqrt[3]{1000}

s = 10

Therefore, the length of a side of the cube is 10 inches.

Conclusion

In this article, we have provided answers to some common questions about the volume of a cube and the length of its sides. We have also explored the relationship between the volume of a cube and the length of its sides, and we have provided examples of how to use the formula for the volume of a cube to find the length of a side of a cube.