Question

When length of each side of a cube is increased by 3 cm, its volume is increased by 2457 $c{m}^3$. Find its side. How much will its volume decrease, if length of each side of it is reduced by 20% ?

• A. $15$ cm, $1647$ $c{m}^3$
• B. $12$ cm, $1647$$c{m}^3$
• C. $17$ cm, $1647$ $c{m}^3$
• D. $13$ cm, $1647$ $c{m}^3$

Answer 1

The correct option is A $15$ cm, $1647$ $c{m}^3$

Let $x$ be the sides of the cube. The the volume will be $x^3$

If the sides are increased by $3$ then length will be $x+3$ and the volume will become $(x+3)\times (x+3)\times (x+3)$. But the volume is increased by $2457$ that is $x^3+2457$

Therefore,

$\Rightarrow (x+3)\times (x+3)\times (x+3)=x^3+2457$

$\Rightarrow x^3+3x^2+6x^2+18x+9x+27=x^3+2457$

$\Rightarrow x^3+9x^2+27x+27=x^3+2457$

$\Rightarrow 9x^2+27x+27=2457$

$\Rightarrow x^2+3x+3=273$

$\Rightarrow x^2+3x-270=0$

$\Rightarrow x^2+18x-15x-270=0$

$\Rightarrow x(x+18)-15(x+18)$

$\Rightarrow (x-15)(x+18)$

$\Rightarrow x=15orx=-18$

Side cannot be negative hence $x=15cm$

With side=$15cm$, then Volume=$3375c{m}^3$

If the side is decreased by $20\%$ then the side decreased will be $\frac{20}{100}\times 15=3cm$

Therefore side=$15-3=12cm$

Volume=$12\times 12\times 12=1728c{m}^3$

Volume decreased=$3375-1728=1647c{m}^3$