Question

If the edge of a cube increases by 20% then find the percentage increase in its volume

Answer 1

Hello,

Let the edge of cube be x
So,
Volume of the cube is x³

The edge increase by 20%
So ,
The new edge is
$x + 20\%of \: x \\ x + \frac{20}{100} x \\ \\ = x + \frac{1}{5} x \\ \\ = \frac{5x + x}{5} = \frac{6x}{5}$
Now,

New cube's volume will be

${ (\frac{6x}{5}) }^{3} \\ \\ = \frac{216 {x}^{3} }{125}$
Now increase in volume is equal to

$\frac{216 {x}^{3} }{125} - {x}^{3} \\ \\ = \frac{216 {x}^{3} - 125 {x}^{3} }{125} \\ \\ = \frac{91 {x}^{3} }{125}$
Now

Increment percentage is equal to

$( \frac{91 {x}^{3} }{125 \times {x}^{3} } \times 100)\% \\ \\ = \frac{91}{125} \times 100 \\ \\ = \frac{91}{5} \times 4 \\ \\ = 18.2 \times 4 \\ = 72.8\%$
So,

The increase in volume is equal to 72. 8 %

Hope this will be helping you ✌️