Question

A metal cube of edge 12 cm is melted and formed into three smaller cubes. If the edges of the two smaller cubes are 6 cm and 8 cm, find the edge of the third smaller cube.

Answer 1

Edge of metal bigger cube = 12 cm
$\therefore$ Volume = $(12{)}^3=1728c{m}^3$
$\therefore$ Sum of volumes of 3 smaller cubes
= 1728 $c{m}^3$
Edge of first smaller cube = 6 cm
$\therefore$ Volume = $(6{)}^3=216c{m}^3$
Edge of second smaller cube = 8 cm
$\therefore$ Volume = $(8{)}^3=512c{m}^3$
Sum of volumes of two smaller cubes
= $1728-728c{m}^3=1000c{m}^3$
$\therefore$ Edge = $\sqrt[3]{31000}=\sqrt[3]{310\times 10\times 10}$
= $\sqrt[3]{3{10}^3}=10cm$