Question

three cubes of iron whose edges are 6 cm, 8 cm and 10 cm,respectively are melted and formed into a single cube. Find the edge of the new cube formed.

Answer 1

Edge of the first cube $=6cm$
volume of the first cube $=(side{)}^3=(6{)}^{3}c{m}^3$
Edge of the second cube $=8cm$
Volume of the second cube $=(side{)}^3=(8{)}^{3}c{m}^3$
Edge of the third cube $=(side{)}^3=(10{)}^{3}c{m}^3$
Let ${}^{\prime }{a}^{\prime }$ be side edge of the new formed cube.
Volume of the cube $=$ Volume of the first cube $+$ volume of the second cube $+$ volume of the third cube
$a^3=6^3+8^3+{10}^3$
$=216+512+1000$
$=1728$
or $a=12$
Edge of the new cube is $12cm.$