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Calculate the gauge pressure (in Pa) at a depth of 115m in seawater. (Density of seawater = 1025 kg/m³, g = 9.8 m/s²) a) 1.11 x 10⁶ Pa
b) 8.34 x 10⁵ Pa
c) 9.20 x 10⁶ Pa
d) 5.67 x 10⁵ Pa

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Hello! I'm the Brainly AI Helper, and I'm here to help you understand how to calculate the gauge pressure at a given depth in seawater. To calculate the gauge pressure at a depth in a fluid, we can use the formula: \[ P = \rho g h \] Where: - \( P \) = gauge pressure (in pascals, Pa) - \( \rho \) = density of the fluid (in kg/m³) - \( g \) = acceleration due to gravity (in m/s²) - \( h \) = depth of the fluid (in meters) Now, let's plug in the values you provided: - Density of seawater, \( \rho = 1025 \, \text{kg/m}^3 \) - Acceleration due to gravity, \( g = 9.8 \, \text{m/s}^2 \) - Depth, \( h = 115 \, \text{m} \) Now substitute these values into the formula: \[ P = 1025 \, \text{kg/m}^3 \times 9.8 \, \text{m/s}^2 \times 115 \, \text{m} \] Calculating this step-by-step: 1. First, calculate \( 1025 \times 9.8 \): \[ 1025 \times 9.8 = 10045 \, \text{kg m/s}^2 \] 2. Next, multiply by the depth (115 m): \[ 10045 \, \text{kg m/s}^2 \times 115 \, \text{m} = 1155175 \, \text{Pa} \] So the gauge pressure at a depth of 115 meters in seawater is: \[ P = 1155175 \, \text{Pa} \] This can be rounded to: \[ P \approx 1.16 \times 10^6 \, \text{Pa} \] Now, let's look at the provided options: a) \( 1.11 \times 10^6 \, \text{Pa} \) b) \( 8.34 \times 10^5 \, \text{Pa} \) c) \( 9.20 \times 10^6 \, \text{Pa} \) d) \( 5.67 \times 10^5 \, \text{Pa} \) The calculated gauge pressure \( 1.16 \times 10^6 \, \text{Pa} \) is closest to option **a)** \( 1.11 \times 10^6 \, \text{Pa} \). So, the answer is: **a) 1.11 x 10⁶ Pa** If you have any further questions or need more clarification, feel free to ask!
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Final answer:

The answer is a) 1.11 x 10⁶ Pa. Use the given values for density of seawater and depth to calculate the gauge pressure in Pa at a depth of 115m in seawater.

Explanation:

The answer is a) 1.11 x 10⁶ Pa. To calculate the gauge pressure in seawater at a depth of 115m, we use the equation:Pg = ρ g h

Where ρ is the density of seawater, g is the acceleration due to gravity, and h is the depth.Plugging in the values (ρ = 1025 kg/m³, g = 9.8 m/s², h = 115m) into the equation, we get the gauge pressure as approximately 1.11 x 10⁶ Pa.

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