A cylindrica bar of metal has a base radius of 2 and a height of 9. It is melted down and reformed into a cube. A side of the cube is

Options

A. 2.32
B. 3.84
C. 4.84
D. 97.21

Explanation

To solve the problem, we need to find the side length of a cube formed by melting a cylindrical bar of metal. Here’s a step-by-step solution:

### Step 1: Calculate the volume of the cylinder
The formula for the volume \( V \) of a cylinder is given by:
\[ V = \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height.

Given:
- Radius \( r = 2 \)
- Height \( h = 9 \)

Substituting the values into the formula:
\[ V = \pi (2)^2 (9) \]
\[ V = \pi (4)(9) \]
\[ V = 36\pi \]

### Step 2: Set the volume of the cube equal to the volume of the cylinder
The volume \( V \) of a cube with side length \( s \) is given by:
\[ V = s^3 \]
Since the volume of the cylinder is equal to the volume of the cube, we have:
\[ s^3 = 36\pi \]

### Step 3: Solve for the side length \( s \)
To find \( s \), we take the cube root of both sides:
\[ s = \sqrt[3]{36\pi} \]

### Step 4: Calculate the value of \( s \)
Using a calculator to find \( \sqrt[3]{36\pi} \):
\[ s \approx \sqrt[3]{36 \times 3.14} \approx \sqrt[3]{113.04} \approx 4.84 \]

### Final Answer
The side length of the cube is approximately \( 4.84 \).

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