Q. 24.7( 13 Votes )

# Three cubes with

Answer :

To find the total surface area of the new cube formed we first need to find its edge

Volume of cube = (edge)^{3}

Volume of cube with edge 8 cm = 8^{3} = 512 cm^{3}

Volume of cube with edge 6 cm = 6^{3} = 216 cm^{3}

Volume of cube with edge 1 cm = 1^{3} = 1 cm^{3}

Let the edge of new cube formed be ‘a’

Volume of new cube = a^{3}

As the three cubes are melted and the new cube is formed

Volume of new cube = volume of all the three cubes

⇒ a^{3} = 512 + 216 + 1

⇒ a^{3} = 729

⇒ a = 9

Surface area of cube = 6 × (edge)^{2}

⇒ surface area of new cube = 6 × a^{2}

= 6 × 9^{2}

= 6 × 81

= 486 cm^{2}

Therefore, surface area of new cube is 486 cm^{2}

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