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Which one of the following is the maximum length of a pencil that can be kept in a rectangular box of dimensions $12 c m × 9 c m × 8 c m$ ?

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13 cm

17 cm

18 cm

19 cm

answer is B.

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Detailed Solution

Given that the length of rectangular box,

l = 12 c m

, breadth of rectangular box,

b = 9 c m

and the height of rectangular box,

h = 8 c m

.
We know that, length of the diagonal of cuboid

= l 2 + b 2 + h 2

………….(1)
Substitution the value of length, breadth and height in equation (1),
Length of the diagonal of cuboid

= 122 + 92 + 82

Length of the diagonal of cuboid

= 144 + 81 + 64

Length of the diagonal of cuboid

= 289

Length of the diagonal of cuboid

= 17 c m

.
Hence, the maximum length of a pencil that can be kept in a rectangular box of dimensions

12 c m × 9 c m × 8 c m

is 17cm.
Therefore, option 2 is correct.

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Which one of the following is the maximum length of a pencil that can be kept in a rectangular box of dimensions 12cm×9cm×8cm ?

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Which one of the following is the maximum length of a pencil that can be kept in a rectangular box of dimensions $12 c m × 9 c m × 8 c m$ ?