Final answer:
The greatest possible volume of the iron block, considering the maximum mass and minimum density, is 0.31 m³ when rounded to two decimal places.
Step-by-step explanation:
To find the greatest possible volume of the iron block, we need to consider the greatest possible mass and the lowest possible density, as volume is calculated by the formula: volume = mass/density. Given that the mass is 2420 kg, correct to the nearest 10 kg, this means the mass could be as much as 2420 kg + 5 kg (the upper boundary of the error margin). Similarly, the density is given as 7900 kg/m³, correct to the nearest 100 kg/m³, and the lowest possible density would be 7900 kg/m³ - 50 kg/m³ (the lower boundary of the error margin). Therefore, the greatest possible volume is calculated from the greatest possible mass and the lowest possible density: volume = (2420 kg + 5 kg) / (7900 kg/m³ - 50 kg/m³).
Largest possible volume = (2420 kg + 5 kg) / (7900 kg/m³ - 50 kg/m³) = 2425 kg / 7850 kg/m³ = 0.30891719745 m³, which is rounded to 0.31 m³ to two decimal places.