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Mathematics

The square on the diagonal of a cube has an area of 1875 sq. cm. Calculate :

(i) the side of the cube.

(ii) the total surface area of the cube.

Mensuration

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Answer

(i) Given:

Area of the square = 1875 cm2

Let a be the side of the square.

Let s be the side of cube.

The square on the diagonal of a cube has an area of 1875 sq. cm. Calculate : Solids, Concise Mathematics Solutions ICSE Class 9.

Area of the square = side2

⇒ a2 = 1875 cm2

⇒ a = 1875\sqrt{1875} cm

⇒ a = 25 3\sqrt{3} cm

Side of the square = Diagonal of the cube

Diagonal of the cube = side 3\sqrt{3}

⇒ s 3\sqrt{3} = 25 3\sqrt{3} cm

⇒ side 3\cancel{\sqrt{3}} = 25 3\cancel{\sqrt{3}} cm

⇒ side = 25 cm

Hence, the side of the cube is 25cm.

(ii) Total surface area of the cube = 6 x side2

= 6 x (25)2 cm2

= 6 x 625 cm2

= 3,750 cm2

Hence, the total surface area of the cube is 3,750 cm2.

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