The maximum length of a pencil that can be kept in a rectangular box of dimensions 8 cm × 6 cm × 2 cm, is:2√13 cm2√14 cm2√26 cm10√2 cm

1. Break Down the Problem

To find the maximum length of a pencil that can fit inside a box, we need to calculate the space diagonal of the rectangular box. The dimensions of the box are given as:

• Length (l) = 8 cm
• Width (w) = 6 cm
• Height (h) = 2 cm

2. Relevant Concepts

The formula for the diagonal $d$ of a rectangular box with dimensions $l$, $w$, and $h$ is given by: $d = \sqrt{l^2 + w^2 + h^2}$

3. Analysis and Detail

Now, we will calculate the diagonal using the given dimensions:

1. Calculate $l^2$: $l^2 = 8^2 = 64$
2. Calculate $w^2$: $w^2 = 6^2 = 36$
3. Calculate $h^2$: $h^2 = 2^2 = 4$
4. Sum the squares: $l^2 + w^2 + h^2 = 64 + 36 + 4 = 104$
5. Take the square root to find the diagonal: $d = \sqrt{104} = \sqrt{4 \times 26} = 2\sqrt{26}$

4. Verify and Summarize

We confirmed all calculations are accurate. Therefore, the maximum length of the pencil that can be kept in the box is $2\sqrt{26} \text{ cm}$.

Final Answer

The maximum length of a pencil that can be kept in the rectangular box is $2\sqrt{26} \text{ cm}$.