three metal cubes of sides 6 8 and 10 cm are melted and formed into a single cube if there is no loss of metal in the process what is the side of the big cube?
answer : 12
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answer : 12
need explanation
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Answer- The above question is from the chapter 'Surface Areas and Volumes'.
Concepts used: 1) Volume of cube with side s = s³ unit³
2) On melting some cubes to form a big cube, the volumes of all smaller cubes is equal to volume of the bigger cube.
Given question: Three metal cubes of sides 6, 8 and 10 cm are melted and formed into a single cube. If there is no loss of metal in the process, what is the side of the big cube?
Solution: Let s₁ = 6 cm
s₂ = 8 cm
s₃ = 10 cm
Let the side of bigger cube be S.
Volume of cube₁ + cube₂ + cube₃ = Volume of bigger cube
6³ + 8³ + 10³ = S³
216 + 512 + 1000 = S³
S³ = 1728
S = ∛1728
S = 12 cm
∴ Side of bigger cube = 12 cm.