Question

Three metal cubes with edges 6 cm, 8 cm and 10 cm respectively are melted together and formed into a single cube. Find the volume, surface area and diagonal of the new cube.

Answer 1

Given : Three metal cubes with edges 6 cm, 8 cm and 10 cm respectively are melted together and formed into a single cube.

Let the length of each edge of the new cube be a cm . Then,  

Volume of cube = a³

(6³ + 8³ + 10³) = a³

⇒ 216 + 512 + 1000 = a³

⇒ 1728 = a³

Volume of the new cube = 1728 cm³

⇒ a = ³√1728  

⇒ a = 12

The length of each edge of the new cube = 12 cm

Surface area of new cube ,S.A = 6a²  

S.A = 6 × 12²

S.A  = 6 × 144

S.A = 864 cm²

Surface area of new cube = 864 cm²

Diagonal of new cube = √3a = √3 × 12 = 12√3 cm  

Hence the volume, surface area and diagonal of the new cube are 1728 cm³ , 864 cm² and 12√3 cm.

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