Question

Three metal cubes with edges 6 cm, 8 cm and 10 cm respectively are melted together and formed into a single cube. Find the volume surface area and diagonal of the new cube.

Answer 1

Edge of first cube = 6 cm

Edge of second cube = 8 cm

and edge of third cube = 10 cm

$\therefore \text{Volume of 3 cubes}=(6{)}^3+(8{)}^3+(10{)}^{3}c{m}^3$

$=216+512+1000c{m}^3$

$=1728c{m}^3$

$\therefore Edgeofsoformedcube$

$=\sqrt[3]{31728}=12cm$

Now surface area = 6 $(side{)}^2$

$=6\times 12\times 12=864c{m}^3$

and length of diagonal =$\sqrt{3}\times side$

$=\sqrt{3}\times 12=12\sqrt{3}cm$