Final answer:
The absolute pressure at the bottom of the swimming pool with a 3.05 m diameter and a water depth of 2.27 m, plus 1.36 atm of atmospheric pressure, is calculated using the fluid pressure equation P = ρgh, resulting in approximately 160063.6 Pascals.
Step-by-step explanation:
To calculate the absolute pressure at the bottom of a swimming pool, we need to consider the atmospheric pressure as well as the pressure exerted by the water above. The diameter of the pool is 3.05 m, so we can find the radius (which is half of the diameter) to be 1.525 m. Next, we'll use the formula for pressure due to a liquid column which is P = ρgh, where ρ is the density of water (approximately 1000 kg/m³), g is the acceleration due to gravity (9.8 m/s²), and h is the depth of the water column (2.27 m in this case). Adding atmospheric pressure (1.36 atm converted to Pascals, with 1 atm = 101325 Pa), we get the following:
P_water = ρgh = (1000 kg/m³)(9.8 m/s²)(2.27 m) = 22266 Pa
Adding the atmospheric pressure (1.36 atm), we have:
P_atm = 1.36 atm × 101325 Pa/atm = 137797.6 Pa
Thus, the total pressure at the bottom of the pool is:
P_total = P_water + P_atm = 22266 Pa + 137797.6 Pa = 160063.6 Pa
Therefore, the absolute pressure at the bottom of the pool is approximately 160063.6 Pascals.