The chambered nautilus is a deepsea creature with a spiral shell that can withstand pressure up to $1180$ pounds per square inch ( $\text{psi}$ ). Underwater pressure consists of atmospheric pressure, which is $14.7\text{psi}$ , plus $0.45\text{psi}$ 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? $\newline$ $\square$

View step-by-step help

Home

Math Problems

Grade 8

Multi-step word problems

Full solution

Q. The chambered nautilus is a deepsea creature with a spiral shell that can withstand pressure up to

1180

pounds per square inch (

\text{psi}

). Underwater pressure consists of atmospheric pressure, which is

14.7\text{psi}

, plus

0.45\text{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?

\newline

\square

Calculate Total Pressure: Determine the total pressure the nautilus shell can withstand. $\newline$ The nautilus shell can withstand a pressure of $1180 \, \text{psi}$ . This includes the atmospheric pressure. $\newline$ Calculation: $1180 \, \text{psi}$ (total pressure the shell can withstand)
Subtract Atmospheric Pressure: Subtract the atmospheric pressure from the total pressure to find the pressure that can be withstood due to water depth alone. $\newline$ The atmospheric pressure is $14.7\,\text{psi}$ , which is always present, whether the nautilus is at the surface or underwater. $\newline$ Calculation: $1180\,\text{psi} - 14.7\,\text{psi} = 1165.3\,\text{psi}$
Calculate Maximum Depth: Calculate the maximum depth the nautilus can go by dividing the pressure due to water depth by the pressure added per foot of depth. $\newline$ The pressure increases by $0.45\,\text{psi}$ for every foot of depth underwater. $\newline$ Calculation: $\frac{1165.3\,\text{psi}}{0.45\,\text{psi/foot}} = 2590\,\text{feet}$
Round to Nearest Foot: Round the depth to the nearest foot. $\newline$ Since we are asked for the depth to the nearest foot, we look at the decimal part of the calculation. If it were $0.5$ or higher, we would round up, but since it is exactly $2590$ feet, no rounding is necessary. $\newline$ Calculation: The depth is already an integer value, so no rounding is needed.