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The chambered nautilus is a deepsea creature with a spiral shell that can withstand pressure up to 1180 pounds per square inch (psi). Underwater pressure consists of atmospheric pressure, which is 14.7psi, plus 0.45psi of hydrostatic pressure per foot of depth under water. To the nearest foot, what is the maximum depth under water at which the shell of a chambered nautilus can withstand the pressure?

The chambered nautilus is a deepsea creature with a spiral shell that can withstand pressure up to 11801180 pounds per square inch (psi). Underwater pressure consists of atmospheric pressure, which is 14.7psi 14.7 \mathrm{psi} , plus 0.45psi 0.45 \mathrm{psi} of hydrostatic pressure per foot of depth under water. To the nearest foot, what is the maximum depth under water at which the shell of a chambered nautilus can withstand the pressure?

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Q. The chambered nautilus is a deepsea creature with a spiral shell that can withstand pressure up to 11801180 pounds per square inch (psi). Underwater pressure consists of atmospheric pressure, which is 14.7psi 14.7 \mathrm{psi} , plus 0.45psi 0.45 \mathrm{psi} of hydrostatic pressure per foot of depth under water. To the nearest foot, what is the maximum depth under water at which the shell of a chambered nautilus can withstand the pressure?
  1. Understand Total Pressure: First, we need to understand the total pressure that the nautilus shell can withstand, which is given as 1180 psi1180 \, \text{psi}. This includes both the atmospheric pressure and the hydrostatic pressure due to the water depth.
  2. Calculate Atmospheric Pressure: The atmospheric pressure is constant at 14.7 psi14.7\,\text{psi}. We need to subtract this from the total pressure the shell can withstand to find out how much pressure is left for the hydrostatic pressure. So, we calculate 1180 psi−14.7 psi1180\,\text{psi} - 14.7\,\text{psi}.
  3. Calculate Hydrostatic Pressure: Performing the subtraction, we get 1180 psi−14.7 psi=1165.3 psi1180 \, \text{psi} - 14.7 \, \text{psi} = 1165.3 \, \text{psi}. This is the amount of pressure that can be attributed to the water depth alone.
  4. Find Maximum Depth: Now, we know that every foot of depth adds 0.45 psi0.45 \, \text{psi} of hydrostatic pressure. To find the maximum depth, we divide the hydrostatic pressure the shell can withstand (1165.3 psi1165.3 \, \text{psi}) by the pressure added per foot of depth (0.45 psi/foot0.45 \, \text{psi/foot}). So, we calculate 1165.3 psi÷0.45 psi/foot1165.3 \, \text{psi} \div 0.45 \, \text{psi/foot}.
  5. Determine Nearest Foot: Performing the division, we get 1165.3 psi÷0.45 psi/foot=2590 feet1165.3 \, \text{psi} \div 0.45 \, \text{psi/foot} = 2590 \, \text{feet}. This is the depth at which the hydrostatic pressure equals the pressure the nautilus shell can withstand. Since the question asks for the maximum depth to the nearest foot, we do not need to round the number because it is already an integer. Therefore, the maximum depth is 2590 feet2590 \, \text{feet}.

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