Question

Three cubes of sides x cm, 8cm and 10cm respectively are melted and formed into a single cube of edge 12cm, Find 'x'.

Answer 1

Given that:
Side (l₁) of cube (a) = x cm
Side (l₂) of cube (b) = 8 cm
Side (l₃) of cube (c) = 10 cm
Edge length of new formed cube = 12cm
Volume of cube (a) = (l₁)³ = x3 cm³
Volume of cube (b) = (l₂)³ = 8³ = 512 cm³
Volume of cube (c) = (l₃)³ = 10³ = 1000 cm³
Total Volume of all three cubes - Volume of 1 cube
x³ + 8³ + 10³ = 12³
x³ + 512 + 1000 = 1728
x³ = 1728 - 1512
x = `root(3)(216)`
∴ x = 6cm.