Final answer:
The pressure at a depth of 256 km in the mantle with a constant density of 3.3 g/cm³ can be calculated using the formula P = ρgh and results in a pressure of 8.255 × 1012 N/m².
Step-by-step explanation:
To calculate the pressure at a depth of 256 km in the mantle, assuming a constant density of the mantle material ρmantle = 3.3 g/cm³, we use the formula for pressure due to a fluid at depth, P = ρgh. First, we need to convert the density of the mantle from g/cm³ to kg/m³, which is 3300 kg/m³ (since 1 g/cm³ = 1000 kg/m³).
Next, we substitute the values into the equation:
- ρ (density) = 3300 kg/m³,
- g (acceleration due to gravity) = 9.81 m/s²,
- h (depth) = 256,000 m (since 1 km = 1000 m).
By calculating P = ρgh, we get:
P = (3300 kg/m³)(9.81 m/s²)(256,000 m),
P = 8.255 × 1012 N/m², which is the pressure at that depth in the mantle.