Question

Question 22

Three cubes of metal whose edges are 6 cm, 8 cm and 10 cm respectively are melted to form a single cube. The edge of the new cube is
(a) 12 cm (b) 24 cm (c) 18 cm (d) 20 cm

Answer 1

The edges of three cubes are 6 cm, 8 cm and 10 cm, respectively.
$\therefore$ Sum of volumes of the three metal cubes
$=6^3+8^3+{10}^3$ $[\because volumeofcube=(edge{)}^3]$
$=216+512+1000$
$=1728c{m}^3$
Since, a new cube is formed by melting these three cubes.
Let a be the side of new cube. Then,
Volume of the new cube = Sum of volumes of three metal cubes
$\Rightarrow a^3=1728$
$\therefore a=12cm$
Hence, the edge of the new cube is 12 cm.