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Question
Three metal cubes with edges 6cm, 8cm and 10cm respectively are melted together and formed into a single cube. Find the diagonal of this cube.
Solution
Given that:
Side (l1) of metal cube (a) = 6cm
Side (l2) of metal cube (b) = 8cm
Side (l3) of metal cube (c) = 10cm
Total Volume of all three cubes = Volume of 1 cube
Volume of cube (a) = (l1)3 = 63 = 216cm3
Volume of cube (b) = (l2)3 = 83 = 512cm3
Volume of cube (c) = (l3)3 = 103 = 1000cm3
Total volume of all three cubes = 1728cm3
∴ Volume of 1 cube = 1728cm3
i.e., l3 = 1728
l = `root(3)(1728)`
∴ Side(l) = 12cm
Length of diagonal of cube
= `sqrt(3) xx "l"`
= `sqrt(3) xx 12`
= `12sqrt(3)"cm"`.
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