Final answer:
The approximate volume of the iron bar with the same mass as the aluminum bar is calculated using the mass and the density of iron. However, the calculated volume of 102.99 cm³ doesn't match the provided options, suggesting a potential error in our calculations or a mismatch with the given options.
Step-by-step explanation:
To find the volume of the iron bar with the same mass as the aluminum bar, we first need to calculate the volume of the aluminum bar based on its dimensions, and then use the densities of both materials to find the volume of the iron bar. Given the density of aluminum is 2.7 g/cm³, we calculate the volume of aluminum bar as:
Volume of aluminum bar = Width x Thickness x Length
= 3.8 cm x 1.3 cm x 61 cm
= 302.66 cm³
Next, we find the mass of the aluminum bar. The mass given is 813.6 grams.
Using the density of iron, which is 7.9 g/cm³, the volume of the iron bar having the same mass can be estimated. The formula to calculate the volume (V) based on mass (m) and density (D) is V = m / D. Therefore, the volume of the iron bar is:
Volume of iron bar = Mass of iron bar / Density of iron
= 813.6 g / 7.9 g/cm³
= 102.99 cm³ (approx.)
The approximate volume of the iron bar that has the same mass as the aluminum bar is 102.99 cubic centimeters. Since this is not one of the options given, we need to double-check our calculations.