Question

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

Answer 1

Three cuboid of dimension $5cm\times 6cm\times 7cm$

$4cm\times 7cm\times 8cm$ & $2cm\times 3cm\times 13cm$

are melted & converted into cube.

Cuboid $1=5cm\times 6cm\times 7cm$ …………$\left(1\right)$

Cuboid $2=4cm\times 7cm\times 8cm$ ………….$\left(2\right)$

Cuboid $3=2cm\times 3cm\times 13cm$ ……………$\left(3\right)$

Now volume of cuboid $(1+2+3)=$ volume of cube $\left(2\right)$

Let 'a' be the edge of cube formed then

Volume of cuboid $1=lbh=210c{m}^3$

Volume of cuboid $2=lbh=224c{m}^3$

Volume of cuboid $3=lbh=78c{m}^3$

From equation $\left(4\right)$ we get

$a^3=210+224+78$

$a^3=512$

$a^3=(8{)}^3$

$[a=8]$

Hence edge of cube is $8$cm.