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
Question
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 cm
- 2√14 cm
- 2√26 cm
- 10√2 cm
Solution
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 of a rectangular box with dimensions , , and is given by:
3. Analysis and Detail
Now, we will calculate the diagonal using the given dimensions:
- Calculate :
- Calculate :
- Calculate :
- Sum the squares:
- Take the square root to find the diagonal:
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 .
Final Answer
The maximum length of a pencil that can be kept in the rectangular box is .
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