Chapter 7, Problem 23P

To determine

Investigate the volume capacity of a barrel of oil in galloons, cubic feet, cubic meters, and the volume capacity of a bushel of agricultural products in cubic inches, cubic feet, and cubic meters.

Answer to Problem 23P

The volume capacity of a barrel of oil in galloons, cubic feet, cubic meters is $\text{42 gallons}$, $5.63{\text{ft}}^3$, $\text{0}\text{.16}{\text{m}}^3$ and the volume capacity of a bushel of agricultural products in cubic inches, cubic feet, and cubic meters is $\text{2150}\text{.4}{\text{in}}^3$, $\text{1}\text{.28}{\text{ft}}^3$, $\text{0}\text{.035}{\text{m}}^3$.

Explanation of Solution

Volume capacity of the Barrel:

Barrel is the wooden container in the form of cylindrical shape. The wooden staves are used to make the barrel by rounding the staves using the hoops. The barrel is in curved shape and the structure is convex and bulges at the center of the barrel which is called as bilge. Such a shape is used to manufacture the barrel in order to roll it and make the roller to change the moving directions with little friction by comparing with the cylinder.

According to the U.S. standard, a barrel contains $42\text{gallons}$ of oil. That is,

$\text{1 barrel}=\text{42 gallons}$

Consider the following expression to calculate the value from gallons to cubic feet,

$\begin{array}{c}\text{1 barrel}=\text{42 gallons}\left[\therefore 1\text{gallon}=\text{0}\text{.134}{\text{ft}}^3\right]\\ =\left(\text{42}\right)\left(\text{0}\text{.134}{\text{ft}}^3\right)\\ =5.63{\text{ft}}^3\end{array}$

Consider the following expression to calculate the value from gallons to cubic meters,

$\begin{array}{c}\text{1 barrel}=\text{42 gallons}\left[\therefore 1\text{gallon}=\text{0}\text{.0038}{\text{m}}^3\right]\\ =\left(\text{42}\right)\left(\text{0}\text{.0038}{\text{m}}^3\right)\\ =\text{0}\text{.16}{\text{m}}^3\end{array}$

Volume capacity of the Bushel:

Bushel is the US customary unit for the mass or weight which is based upon the measure of dry capacity. It is a unit of units used for measurement of agricultural products such as corn, beans, flaxseeds etc.

According to the U.S. standard, a bushel contains $8\text{gallons}$. That is,

$\text{1 bushel}=\text{8 gallons}$

Consider the following expression to calculate the value from dry gallons to cubic inches in dry capacity,

$\begin{array}{c}\text{1 bushel}=\text{8 gallons}\left[\therefore 1\text{gallon}=\text{268}\text{.8}{\text{in}}^3\right]\\ =\left(\text{8}\right)\left(\text{268}\text{.8}{\text{in}}^3\right)\\ =\text{2150}\text{.4}{\text{in}}^3\end{array}$

Consider the following expression to calculate the value from dry gallons to cubic feet,

$\begin{array}{c}\text{1 bushel}=\text{8 gallons}\left[\therefore 1\text{gallon}=\text{0}\text{.16}{\text{ft}}^3\right]\\ =\left(\text{8}\right)\left(\text{0}\text{.16}{\text{ft}}^3\right)\\ =\text{1}\text{.28}{\text{ft}}^3\end{array}$

Consider the following expression to calculate the value from dry gallons to cubic meters,

$\begin{array}{c}\text{1 bushel}=\text{8 gallons}\left[\therefore 1\text{gallon}=\text{0}\text{.0044}{\text{m}}^3\right]\\ =\left(\text{8}\right)\left(\text{0}\text{.0044}{\text{m}}^3\right)\\ =\text{0}\text{.035}{\text{m}}^3\end{array}$

The volume capacity of a barrel of oil in galloons, cubic feet, cubic meters is $\text{42 gallons}$, $5.63{\text{ft}}^3$, $\text{0}\text{.16}{\text{m}}^3$ and the volume capacity of a bushel of agricultural products in cubic inches, cubic feet, and cubic meters is $\text{2150}\text{.4}{\text{in}}^3$, $\text{1}\text{.28}{\text{ft}}^3$, $\text{0}\text{.035}{\text{m}}^3$.

The barrel is the old unit to measure the volume of oil, fluid or dry barrels. It is used to measure the bulk amount of containers especially in U.S and U.K.

Bushel is the US customary unit of volume for the mass, used to measure the bulk range of mass in volume used specially in U.S and UK.

The relation in both volume units is $1\text{ U}\text{.S dry barrel = 3}\text{.28 US bushels}$.

And $1\text{ U}\text{.S bushel= 7}\text{.7515 imperial gallons}$, therefore

$\begin{array}{l}1\text{ U}\text{.S dry barrel = 3}\text{.28 }\left(\text{7}\text{.7515 imperial gallons}\right)\\ 1\text{ U}\text{.S dry barrel = 25}\text{.425 imperial gallons}\end{array}$

The American merchants are used to measure the products in Barrels and Bushels.

Conclusion:

Thus, the volume capacity of a barrel of oil in galloons, cubic feet, cubic meters is $\text{42 gallons}$, $5.63{\text{ft}}^3$, $\text{0}\text{.16}{\text{m}}^3$ and the volume capacity of a bushel of agricultural products in cubic inches, cubic feet, and cubic meters is $\text{2150}\text{.4}{\text{in}}^3$, $\text{1}\text{.28}{\text{ft}}^3$, $\text{0}\text{.035}{\text{m}}^3$.