Question

What will happen to the volume of a cube, if its edge is halved ?

Answer 1

\[\text { Suppose that the length of the edge of the cube is x } . \]

\[\text { Then, volume of the cube = (side  })^3 = x^3 \]

\[\text { When the length of the side is halved, the length of the new edge becomes  }\frac{x}{2}.\]

\[\text { Now, volume of the new cube = (side  })^3 = \left( \frac{x}{2} \right)^3 =\frac{x^3}{2^3}=\frac{x^3}{8}=\frac{1}{8} \times x^3 \]

\[\text { It means that if the edge of a cube is halved, its new volume will be } \frac{1}{8} \text  { times the initial volume } . \]