If a rectangular paper of length 6 cm. and width 3 cm. is rolled to form a cylinder with height equal to the width of the paper, then its base radius is

Options

A. `(6)/(pi)` cm
B. `(3)/(pi)` cm
C. `(3)/(2 pi )` cm
D. `(9)/(2 pi) ` cm

Answer

To find the base radius of the cylinder formed by rolling a rectangular paper of length 6 cm and width 3 cm, we can follow these steps:

### Step 1: Identify the dimensions of the rectangular paper
The rectangular paper has:
- Length (L) = 6 cm
- Width (W) = 3 cm

### Step 2: Understand the formation of the cylinder
When the rectangular paper is rolled to form a cylinder:
- The height (h) of the cylinder is equal to the width of the paper, which is 3 cm.
- The length of the paper becomes the circumference (C) of the base of the cylinder.

### Step 3: Calculate the circumference of the base of the cylinder
The circumference of the base of the cylinder is given by the length of the paper:
\[ C = L = 6 \text{ cm} \]

### Step 4: Relate the circumference to the radius
The circumference of a circle is given by the formula:
\[ C = 2\pi r \]
Where \( r \) is the radius of the base of the cylinder.

### Step 5: Solve for the radius
We can set the circumference equal to the length of the paper:
\[ 2\pi r = 6 \]

Now, we can solve for \( r \):
\[ r = \frac{6}{2\pi} \]
\[ r = \frac{3}{\pi} \]

### Step 6: Approximate the value of the radius
Using \( \pi \approx 3.14 \):
\[ r \approx \frac{3}{3.14} \approx 0.955 \text{ cm} \]

### Final Answer
The base radius of the cylinder is approximately \( \frac{3}{\pi} \) cm or about 0.955 cm.

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