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The longest rod that can be placed in the cubical vessel is measured as $83$ cm. The surface area of the cube is

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192 cm 2

384 cm 2

512 cm 2

768 cm 2

answer is B.

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Detailed Solution

It is given that the longest rod that can be placed in the cubical vessel is measured as

83

cm.
We know that the length of diagonal of a cube

= a 3,

where

a

is the length of the cube.
The total surface area of a cube,

TSA = 6 a 2 .

From the given length of a diagonal, we can calculate the length of the side of the cube as,

a 3 = 83 ⇒ a = 8 cm

Now, we can easily calculate the total surface area of the cube as shown:

TSA = 6 a 2 = 6 8 × 8 cm 2 = 384 cm 2

Therefore the surface area of the cube is

384 cm 2 .

Hence, option (2) is correct.

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