The length of a pencil is `16 cm` and its diameter is `6 mm`. What is the ratio of the diameter of the pencil to that of its length?

Options

A. `7: 80`
B. `3: 80`
C. `9: 80`
D. `7: 50`

Explanation

To find the ratio of the diameter of the pencil to its length, we will follow these steps:

### Step 1: Identify the given measurements
- Length of the pencil = 16 cm
- Diameter of the pencil = 6 mm

### Step 2: Convert the measurements to the same unit
Since the length is in centimeters and the diameter is in millimeters, we need to convert one of them to the same unit. We will convert the length from centimeters to millimeters.

1 cm = 10 mm

So, to convert 16 cm to mm:
\[ 16 \text{ cm} = 16 \times 10 \text{ mm} = 160 \text{ mm} \]

### Step 3: Write the ratio of the diameter to the length
Now we have both measurements in millimeters:
- Diameter = 6 mm
- Length = 160 mm

The ratio of the diameter to the length is:
\[ \text{Ratio} = \frac{\text{Diameter}}{\text{Length}} = \frac{6 \text{ mm}}{160 \text{ mm}} \]

### Step 4: Simplify the ratio
To simplify the ratio \( \frac{6}{160} \), we need to find the greatest common divisor (GCD) of 6 and 160.

Both numbers can be divided by 2:
\[ \frac{6 \div 2}{160 \div 2} = \frac{3}{80} \]

### Step 5: State the final ratio
Thus, the ratio of the diameter of the pencil to its length is:
\[ 3 : 80 \]