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Question
Three cubes of iron whose edges are 6 cm, 8 cm and 10 cm, respectively are melted and formed into a single cube. Find the edge of the new cube formed.
Solution
We have,
Edges of the cubes : a1 = 6 cm, a2 = 8 cm and a3 = 10 cm
Let the edge of the new cube so formed `= a_1^3 + a_2^3 + a_3^3`
⇒ a3 = 63 + 83 + 103
⇒ a3 = 216 + 512 + 1000
⇒ a3 = 1728
`⇒ a = root(3)(1728)`
∴ a = 12 cm
So, the edge of the new cube so formed is 12 cm.
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