Question

If each edge of a cube is decreased by $30\%$ then, find the corresponding decrease in volume

Answer 1

Let the side of cube be $a$

Volume of cube is $a^3$

Edge is decreased by $30\%$

So the side is,

$a-\frac{30}{100}a=a(1-\frac{3}{10})=\frac{7a}{10}$

Volume of the cube is= ${\left(\frac{7a}{10}\right)}^3=\frac{343a^3}{1000}$

Change in volume$=a^3-\frac{343a^3}{1000}=\frac{657a^3}{1000}$

So, decreased percent of volume is given by $=\frac{\frac{657a^3}{1000}}{a^3}\times 100=\frac{657}{1000}\times 100=65.7\%$