(b) A cube with volume $$ 1728 \mathrm{~cm}^{3} $$

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To find the side length of a cube with a given volume, we can use the formula for the volume of a cube:

$$ V = s^3 $$

where:
- $$ V $$ is the volume of the cube,
- $$ s $$ is the side length of the cube.

Given that the volume of the cube is $$ 1728 \, \text{cm}^3 $$, we can substitute this value into the formula and solve for the side length $$ s $$.

$$ 1728 = s^3 $$

Now, we can solve for $$ s $$ by taking the cube root of both sides of the equation.
Calculate the value by following steps:
- step0: Calculate:
  $$1728^{\frac{1}{3}}$$
- step1: Factor the number:
  $$\left(12^{3}\right)^{\frac{1}{3}}$$
- step2: Evaluate the power:
  $$12$$
The side length of the cube is $$ 12 \, \text{cm} $$.

(b) A cube with volume \( 1728 \mathrm{~cm}^{3} \)

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