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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.
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Solution
Let the length of each edge of the new cube be a cm
Then,
`a^3=(6^3+8^3+10^3)cm^3`
`⇒ a^3= 1728`
`⇒ a = 12`
∴ Volume of new cube=`=a^3=1728cm^3`
Surface area of the new cube `6a^2=6xx12^2cm^2`
`= 864 cm^2`
Diagonals of the new cube = `sqrt(3a)= 12 sqrt3cm.`
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