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Mathematics

The area of a square on the diagonal of a cube is 48 cm2. Each edge of the cube is :

  1. 2 cm

  2. 4 cm

  3. 6 cm

  4. 8 cm

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Answer

Given:

Area of the square = 48 cm2

Let a be the side of square.

The area of a square on the diagonal of a cube is 48 cm2. Each edge of the cube is : Solids, Concise Mathematics Solutions ICSE Class 9.

Area of square = side2

⇒ a2 = 48 cm2

⇒ a = 48\sqrt{48} cm

⇒ a = 16×3\sqrt{16 \times 3} cm

⇒ a = 4 3\sqrt{3} cm

Let s be the side of cube.

Diagonal of cube = side 3\sqrt{3}

⇒ Side of square = Diagonal of cube

⇒ s 3\sqrt{3} = 4 3\sqrt{3} cm

⇒ s 3\cancel{\sqrt{3}} = 4 3\cancel{\sqrt{3}} cm

⇒ side = 4 cm

Each edge of the cube is 4 cm.

Hence, option 2 is the correct option.

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