Cubes: Calculate The Missing Side based on the formula

To solve this problem, we need to find the side length of the cube given that its volume is 1331 cubic units.

We use the formula for the volume of a cube:
$V = a^3$

Here, the volume $V$ is 1331, so substituting into the formula gives:
$1331 = a^3$

To find $a$, take the cube root of both sides:
$a = \sqrt[3]{1331}$

Calculating the cube root, we find:
$a = 11$

Thus, the side length of the cube is $\mathbf{11}$. This corresponds to choice 3 from the options provided.

To solve for the side length of a cube with a volume of 27 cm³, we will apply the formula for the volume of a cube:

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

$V = a^3$

where $V$ is the volume, and $a$ is the length of each side.

Given $V = 27$ cm³, we can solve for $a$ by taking the cube root of the volume:

$a = \sqrt[3]{V}$

Substituting the given volume, we have:

$a = \sqrt[3]{27}$

Calculating the cube root, we find:

$a = 3$

Thus, the length of each side of the cube is $3$ cm.

To solve this problem, we'll follow these steps:

• Step 1: Identify the given information.
• Step 2: Apply the appropriate formula for the surface area of a cube.
• Step 3: Solve the equation to find the side length.

Now, let's work through each step:

Step 1: The problem gives us that the surface area of the cube is 24 cm².

Step 2: We'll use the formula for the surface area of a cube: $A = 6s^2$, where $A$ is the surface area and $s$ is the side length.

Step 3: Substitute the given surface area into the formula and solve for $s$:

$6s^2 = 24$

Divide both sides by 6 to isolate $s^2$:

$s^2 = \frac{24}{6} = 4$

Take the square root of both sides to solve for $s$:

$s = \sqrt{4} = 2$

Therefore, the solution to the problem is $s = 2$ cm.

To solve the problem of finding the length of the cube's edges, we begin with the formula for the volume of a cube, which is:

$V = a^3$

where $V$ is the volume and $a$ is the length of one edge of the cube.

Given that the volume $V$ is 27 cm$^3$, we can substitute it into the formula:

$27 = a^3$

To solve for $a$, we need to take the cube root of both sides of the equation:

$a = \sqrt[3]{27}$

Since 27 is a perfect cube (as $27 = 3^3$), the cube root of 27 is 3. Thus,

$a = 3$ cm

Therefore, the length of each edge of the cube is $\mathbf{3}$ cm.

To find the length of an edge of the cube given its volume, we'll proceed with the following steps:

• Step 1: Identify the volume of the cube.
• Step 2: Use the formula for the volume of a cube to find the edge length.
• Step 3: Calculate the cube root of the volume.

Step 1: The volume of the cube is given as $8$ cm$^3$.

Step 2: We use the formula for the volume of a cube:
$V = a^3$,
where $V$ is the volume and $a$ is the length of the edge.

Step 3: To find the edge length $a$, we need to take the cube root of the volume:
$a = \sqrt[3]{V} = \sqrt[3]{8}$

Calculating the cube root, we find:
$a = 2$

Therefore, the length of the edge of the cube is $2$ cm.

To solve this problem, we'll follow these steps:

• Step 1: Identify the formula for the volume of a cube.
• Step 2: Apply the formula with given values.
• Step 3: Calculate the cube root to find the edge length.

Now, let's work through each step:

Step 1: The volume of a cube is given by the formula $V = a^3$, where $a$ is the edge length.

Step 2: We are given the volume $V = 1 \, \text{cm}^3$. Therefore, we have $1 = a^3$.

Step 3: To find $a$, we take the cube root of both sides of the equation:

$a = \sqrt[3]{1} = 1 \, \text{cm}$.

Thus, the edge length of the cube is $\mathbf{1 \, \text{cm}}$.

To find the length of the edges of the cube, we will utilize the relationship between the volume and the edge length for a cube. Specifically, the volume $V$ of a cube with edge length $a$ is given by the formula:

$V = a^3$

Given that the volume of the cube is 64 cm³, we set up the equation:

$a^3 = 64$

To solve for $a$, we need to find the cube root of 64:

$a = \sqrt[3]{64}$

Recognizing that 64 is a perfect cube, we can confirm that:

$\sqrt[3]{64} = 4$

Thus, the length of each edge of the cube is 4 cm.

This solution matches option 3, which is 4 cm, as the correct choice.

To solve this problem, we will follow these steps:

• Step 1: Identify the given information.
• Step 2: Apply the appropriate formula.
• Step 3: Perform the necessary calculations to determine the length of the edge.

Now, let's work through each step:
Step 1: The problem gives us the volume of the cube as $125 \, \text{cm}^3$.
Step 2: The formula for the volume of a cube is $V = a^3$, where $a$ is the length of a side of the cube.
Step 3: We substitute the given volume into the formula: $125 = a^3$. Solving for $a$, take the cube root of both sides:

$a = \sqrt[3]{125}$

Recognizing $125$ as a perfect cube, we have $125 = 5^3$. Therefore,

$a = 5 \, \text{cm}$

Thus, the length of each edge of the cube is $5 \, \text{cm}$.

This matches the correct choice from the multiple options provided, confirming our calculations.

The solution to the problem is $a = 5 \, \text{cm}$.

To find the length of the edge of a cube with a volume of 216 cm$^3$, we need to find the cube root of 216.

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

• $\text{Volume} = s^3$, where $s$ is the length of an edge of the cube.

We are given the volume $216 \, \text{cm}^3$, so we set up the equation:

• $s^3 = 216$

To solve for $s$, we take the cube root of both sides of the equation:

$s = \sqrt[3]{216}$

Calculating the cube root of 216, we find:

• $\sqrt[3]{216} = 6$

Therefore, the length of each edge of the cube is $6$ cm.

The correct answer to the problem is $6$ cm.

To solve the problem, follow these steps:

• Step 1: Identify the given volume of the cube, $V = 1000$ cm³.
• Step 2: Use the formula for the volume of a cube, $V = a^3$, to set up the equation $a^3 = 1000$.
• Step 3: Solve for $a$ by taking the cube root of 1000, i.e., $a = \sqrt[3]{1000}$.

Let's compute the cube root:

$a = \sqrt[3]{1000} = 10$.

Therefore, the length of each edge of the cube is $10$ cm.

To solve this problem, we'll use the relationship between the volume of a cube and its edge length, given by the formula:

$V = s^3$

where $V$ is the volume and $s$ is the edge length.

We are given that the volume of the cube is 343 cm³. We need to solve for the edge length $s$:

$s^3 = 343$

To find $s$, we take the cube root of both sides of the equation:

$s = \sqrt[3]{343}$

We need to determine the cube root of 343. Knowing that $7 \times 7 \times 7 = 343$, we find:

$s = 7$ cm

Therefore, the length of each edge of the cube is $7$ cm.

To determine the length of one edge of a cube with a volume of 512 cm³, we follow these steps:

• Step 1: Understand the relationship between volume and edge length for a cube. The volume $V$ is given by the formula $V = s^3$, where $s$ is the edge length.
• Step 2: Replace the volume in the formula with the given value: $512 = s^3$.
• Step 3: To find $s$, take the cube root of both sides of the equation: $s = \sqrt[3]{512}$.
• Step 4: Calculate the cube root of 512. Factoring 512, we find $512 = 8 \times 8 \times 8$, so $\sqrt[3]{512} = 8$.

Thus, the length of each edge of the cube is $8$ cm.