Question

Each side of a cube is decreased by 50%. Let us calculate the ratio of the volumes of the original cube and the changed cube

January 1, 2024

Answer

Let one side of a cube = x cm.

∴ Its volume = x³ cu.cm.

If the length is reduced by 50% then the new length of the cube $=\frac{x}{2}$ cm.

∴ Volume of the new cube $=(\frac{x}{2} cm)^3=\frac{x^3}{8}$

∴ The ratio of the volume of the original cube & volume of the new cube

$=x^3: \frac{x^3}{8}=1: \frac{1}{8}$ = 8 : 1

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