Question

If the edge of a cube is increased by $2cm$, the volume will increase by $488{cm}^2$. What then will be the new length of each edge of the cube

Answer 1

Let the length of the edge of the cube be $x$

Length after $2cm$ increase $=x+2$

Then original Volume of the cube $=$ (Length)${}^3$

That is, Volume $=x^3$

New Volume $=(x+2{)}^3$

Given that after increasing the length of the edge, the volume is increased by $488c{m}^2$

$\Rightarrow (x+2{)}^3-x^3=488$

$\Rightarrow x^3+6x^2+12x+8-x^3=488$

$\Rightarrow 6x^2+12x-480=0$

$\Rightarrow x^2+2x-80=0$

$\Rightarrow (x-8)(x+10)=0$

$\Rightarrow x=8orx=-10(x\ne -10,xcannotbenegative)$

Therefore the length of each edge of the cube is $8+2=10cm$