Three cubes of sides 6 cm, 8 cm and 1 cm are melted to form a new cube. The surface area of the new cube is:‐
1. 486 sq cm
2. 496 sq cm
3. 586 sq cm
4. 658 sq cm
1. 486 sq cm
2. 496 sq cm
3. 586 sq cm
4. 658 sq cm
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Correct Answer – Option 1 : 486 sq cm
Surface area of cube = 6 × a2, where a is side of the cube
Volume of cube = a3
Volume of cube with side 1 cm = 13 = 1 cm3
Volume of cube with side 6 cm = 63 = 216 cm³
Volume of cube with side 8 cm = 83 = 512 cm³
Total Volume = 1 + 216 + 512 = 729 cm³
Side of new cube = a cm
Volume of new cube = a³ cm³
a³ = 729
⇒ a = 9
Side of cube = 9 cm
Surface Area = 6 × a² = 6 × 9² = 486 cm²
∴ Surface area of the new formed cube 486 cm2