Question

If the length of each side of a cube is reduced by one-third of its original volume, then express its new volume as a fraction of its original volume.

• A. $\frac{7}{27}$
• B. $\frac{1}{27}$
• C. $\frac{5}{13}$
• D. $\frac{8}{27}$

Answer 1

The correct option is D $\frac{8}{27}$

Volume of cube is $x^3{m}^3$
If its length is reduced to one-third of its original length.
Then , the new length of the cube is $=\frac{2x}{3}$
Then, the new volume of the cube is ${\left(\frac{2x}{3}\right)}^3=\frac{8x^3}{27}$
Therefore, The new volume of the cube is $\frac{8}{27}\left(oldvolumeofcube\right)$.