Final answer:
The density of the bronze alloy is calculated using the weighted average of the densities of copper and tin based on their mass percentages in the mixture. With 75% copper and 25% tin, the calculated density of the bronze is 8150kg/m³.
Step-by-step explanation:
To calculate the density of a bronze alloy when given the mass percentages and densities of its constituent metals, we can use the concept of weighted average. Given that we have 200kg of bronze with 75% copper and 25% tin, the masses of copper and tin are 150kg and 50kg respectively.
The density of copper is 8900kg/m³, and for tin, it's 7000kg/m³. We can use the formula for the density of a mixture:
Density of bronze = (Mass of copper × Density of copper + Mass of tin × Density of tin) / Total mass of the mixture
Plugging in the numbers: Density of bronze = (150kg × 8900kg/m³ + 50kg × 7000kg/m³) / 200kg
Calculating the above expression, we get Density of bronze = (1335000kg/m³ + 350000kg/m³) / 200kg = 8150kg/m³
Therefore, the correct answer is (c) 8150kg/m³.