Question

Three cuboids of dimensions $5cm\times 6cm\times 7cm,4cm\times 7cm\times 8cm\times$ and $2cm\times 3cm\times 13cm$ are melted and a cube is made. Find the of cube.

Answer 1

Dimensions of first cubiod
= $5cm\times 6cm\times 7cm$
$\therefore Volume=5\times 6\times 7=210c{m}^3$
Dimension of second cubiod
= $4cm\times 7cm\times 8cm$
$\therefore Volume=4\times 7\times 8=224c{m}^3$
Dimension of third cubiod
= $2cm\times 3cm\times 13cm$
$\therefore Volume=2\times 3\times 13=78c{m}^3$
Total volume of three cubes
= 210+224+78 $c{m}^3=512c{m}^3$
$\therefore$ Volume of cube = $512c{m}^3$
$\therefore$ Side of cube = $\sqrt[3]{3512}=\sqrt{8\times 8\times 8}$
= $\sqrt[3]{38^3}=8cm$