Question

The volume of a cube will be reduced to ____ of its original volume, if its length is reduced to $\frac{1}{3}$rd of its original length.

• A. $\frac{1}{3}$
• B. $\frac{1}{9}$
• C. $\frac{1}{27}$
• D. $\frac{1}{81}$

Answer 1

The correct option is C $\frac{1}{27}$

Let the length of each side of a cube be 'a', then its volume $=a^3$ [$\because$ volume of a cube $=(side{)}^3$]
If its side length is reduced to one third, then length of its side $=a\times \frac{1}{3}=\frac{a}{3}$
Now, its volume $={\left(\frac{a}{3}\right)}^3=\frac{a^3}{27}$
Hence, new volume $\frac{1}{27}$ times of original volume.