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Three solid iron cubes of edges 6 cm, 7 cm, and 8 cm are melted together to make a new cube. 71 cm3 of the melted material is lost due to improper handling. The area of the whole surface of the newly formed cube is:
1. 294 cm2
2. 600 cm2
3. 343 cm2
4. 729 cm2

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Correct Answer - Option 2 : 600 cm2

Given:

Three solid iron cubes of edges 6 cm, 7 cm, and 8 cm.

71 cm3 of the melted material is lost due to improper handling.

Concept:

The volume of cube = a3

The total surface area of cube = 6a2

Where a = side

When a figure melted together to make a new figure then the volume is equal.

Explanation:

Volume of three solid cube = Volume of a new cube

V = 63 + 73 + 83 = 216 + 343 + 512 = 1071 cm3

(∵ 71 cm3 of the melted material is lost due to improper handling)

So volume of new cube (a3) = 1071 - 71 = 1000 cm3

⇒ a = 10 cm

Total surface area of volume = 6a2 = 6 × 102

∴ The total surface area of new cube is 600 cm2.

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