Question

If the length of a diagonal of a cube is 8 cm, then its surface area is
A. 512 cm²
B. 384 cm²
C. 192 cm²
D. 768 cm²

Answer 1

Given : The length of a diagonal of a cube is 8√3 cm. (Mistake in the question)

Diagonal of a cube = √3a

8√3 = √3a

8 = a  

Edge of a cube , a = 8 cm.

Surface area of cube = 6a²

Surface area of cube = 6 × 8²

Surface area of cube = 6 × 64

Surface area of cube = 384 cm²

Hence the Surface area of a cube is 384 cm².

Option (B) 384 cm² is correct.

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Answer 2

Diagonal = 8_/3 cm

Diagonal of a cube = (_/3)a

Where a is the side of the cube

=> 8_/3 = _/3a

=> a = 8 cm

Surface Area = 6a^2 = 6 × 8 × 8 = 6 × 64 = 384 sq cm

Answer is:- (B) 384 sq cm