Question

A cube with a volume of 64 cubic meters is scaled by a factor of 5. What is the volume of the modified cube in meters

Answer 1

8,000

Explanation:

When the sides of the cube are scaled by a factor of k, the volume increases by a factor of k3. Here, the new volume is 64 cubic meters × 53 = 8,000 cubic meters.

Answer 2

`\bf \textit{volume of a cube}\\ V=s^3~~ \begin{cases} s=&side's\\ &length\\ \cline{1-2} V=&64 \end{cases}\implies 64=s^3\implies \sqrt[3]{64}=s\implies \boxed{4=s} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{scaling all sides by a factor of 5}}{V=s^3\implies V=(4\cdot 5)^3}\implies V=20^3\implies V=8000`