What is the edge length of a cube whose volume is `4,096 cm^(3)` ?

Options

A. 16 cm
B. 1,365.33 cm
C. 64 cm
D. 455.11 cm

Explanation

To find the edge length of a cube whose volume is \(4096 \, \text{cm}^3\), we can follow these steps:

### Step 1: Understand the formula for the volume of a cube
The volume \(V\) of a cube is given by the formula:
\[ V = a^3 \]
where \(a\) is the length of an edge of the cube.

### Step 2: Set the volume equal to the given value
We know that the volume of the cube is \(4096 \, \text{cm}^3\). Therefore, we can set up the equation:
\[ a^3 = 4096 \]

### Step 3: Solve for \(a\) by finding the cube root
To find the edge length \(a\), we need to take the cube root of both sides of the equation:
\[ a = \sqrt[3]{4096} \]

### Step 4: Calculate the cube root
Now we need to calculate \( \sqrt[3]{4096} \). We can do this by recognizing that \(4096\) is a perfect cube.

To find the cube root:
1. Factor \(4096\) into its prime factors.
2. We find that \(4096 = 16 \times 16 \times 16\) or \(16^3\).
3. Therefore, \( \sqrt[3]{4096} = 16 \).

### Step 5: State the final answer
Thus, the edge length \(a\) of the cube is:
\[ a = 16 \, \text{cm} \]

### Summary
The edge length of the cube is \(16 \, \text{cm}\).

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