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A cube's diagonal measures $83$ cm long.

What is its surface area?

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512 cm

2

384 cm

2

192 cm

2

768 cm

2

answer is B.

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Detailed Solution

Given that, the diagonal of the cube is

83 c m

.
First we will calculate the length of the side of a cube from diagonal length.
Length of diagonal of a cube

= 3 a

⇒ 83 = 3 a

On comparing both the sides, we get,

⇒ a = 8

The formula that we will require to solve this question is-
Areas of a cube

= 6 a 2

Now, we will calculate the area using obtained length-

⇒ A = 6 a 2

⇒ A = 6 × 82

⇒ A = 384 c m 2

Therefore, the surface area of the cube is

384 c m 2

Hence, option 2 is the correct option.

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