Final answer:
The side measurement of the titanium cube is not accurately reflected by the provided options. Using the density of titanium, the calculated side length is approximately 6.8 cm, which is not listed as an option.
Step-by-step explanation:
To determine the side measurement of a titanium cube with a mass of 1,415 g, we need to use the density of titanium. The density (ρ) of titanium is approximately 4.506 g/cm³. The formula for the volume (V) of a cube is V = s³ where s is the side length. Since density is mass (m) divided by volume, we have ρ = m/V, which we can rearrange to find V = m/ρ.
By substituting the mass of the titanium cube into the formula, we have V = 1,415 g / 4.506 g/cm³, which equals approximately 314.025 cm³. Now, we take the cube root to find the side length: s = ∛(V) = ∛(314.025 cm³) which is approximately 6.8 cm. This does not match any of the options provided (a) 11 cm, (b) 12 cm, (c) 13 cm, (d) 14 cm, indicating a possible error in the question or the provided options.