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Question
What will happen to the volume of a cube, if its edge is halved ?
Solution
\[\text { Suppose that the length of the edge of the cube is x } . \]
\[\text { Then, volume of the cube = (side })^3 = x^3 \]
\[\text { When the length of the side is halved, the length of the new edge becomes }\frac{x}{2}.\]
\[\text { Now, volume of the new cube = (side })^3 = \left( \frac{x}{2} \right)^3 =\frac{x^3}{2^3}=\frac{x^3}{8}=\frac{1}{8} \times x^3 \]
\[\text { It means that if the edge of a cube is halved, its new volume will be } \frac{1}{8} \text { times the initial volume } . \]
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