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.

Answer 1

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"`.