The Total Length of the Pencil

To find the total length of the pencil, we need to consider the different proportions of black, white, and blue segments in the pencil. Let's break down the given information step by step:

1. Black Segment
- It is given that 1/8 of the pencil is black.
- Let's assume the length of the black segment as 'x'.

2. White Segment
- It is stated that 1/2 of the remaining length after the black segment is white.
- After deducting the black segment, the remaining length of the pencil is (1 - 1/8) = 7/8.
- Therefore, the length of the white segment is (1/2) * (7/8) = 7/16.

3. Blue Segment
- The remaining length of the pencil after the black and white segments is 3 1/2.
- This can also be written as (3 + 1/2) = 7/2.
- Therefore, the length of the blue segment is 7/2.

4. Total Length Calculation
To find the total length of the pencil, we need to add up the lengths of the black, white, and blue segments.

- Black segment length: x
- White segment length: 7/16
- Blue segment length: 7/2

The total length of the pencil is obtained by adding these three segments together:

x + 7/16 + 7/2

However, since we do not have a specific value for the black segment length (x), we cannot determine the exact total length of the pencil.

is the answer 4.1 cm