KnowledgeBoat Logo

Mathematics

Three cubes whose edges are x cm, 8 cm and 10 cm respectively are melted and recast into a single cube of edge 12 cm. Find x.

Mensuration

20 Likes

Answer

Since, cubes are melted and recasted into a single cube.

∴ Total volume of three cubes = Volume of new single cube

Substituting values we get,

⇒x3+83+103=123⇒x3+512+1000=1728⇒x3+1512=1728⇒x3=216⇒x3=63⇒x=6.\Rightarrow x^3 + 8^3 + 10^3 = 12^3 \\[1em] \Rightarrow x^3 + 512 + 1000 = 1728 \\[1em] \Rightarrow x^3 + 1512 = 1728 \\[1em] \Rightarrow x^3 = 216 \\[1em] \Rightarrow x^3 = 6^3 \\[1em] \Rightarrow x = 6.

Hence, x = 6.

Answered By

14 Likes

Related Questions