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Mathematics

The diagonal of a cube is 25325\sqrt{3} m. Find its surface area.

Surface Area, Volume, Capacity

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Answer

Given:

The diagonal of a cube = 25325\sqrt{3} m

Let s be the side of cube.

As we know that the diagonal of the cube = 3\sqrt{3} x side

3×s=2533×s=25×3s=25⇒ \sqrt{3} \times s = 25\sqrt{3}\\[1em] ⇒ \cancel{\sqrt{3}} \times s = 25 \times \cancel{\sqrt{3}}\\[1em] ⇒ s = 25

As we know, the surface area of cube = 6 x side2

= 6 x (25)2 m2

= 6 x 625 m2

= 3,750 m2

Hence, the surface area of the cube is 3,750 m2.

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