Questions: The United States currently imports 9.5 x 10^6 barrels of oil each day. If a cylindrical storage tank were to be constructed with a base of diameter 41 ft. With 1.0 barrel = 42 gals, answer the following questions. What would be the height of the container to store this daily consumption? (Round the final answer to two decimal places.) The height of the container is ft.

Solution Steps

To find the height of the cylindrical storage tank that can store the daily oil consumption, we need to follow these steps:

1. Convert the daily oil consumption from barrels to gallons.
2. Calculate the volume of the cylindrical tank in cubic feet.
3. Use the formula for the volume of a cylinder \( V = \pi r^2 h \) to solve for the height \( h \).

The daily oil consumption in barrels is given as \( 9.5 \times 10^{6} \) barrels. To convert this to gallons, we use the conversion factor \( 1 \text{ barrel} = 42 \text{ gallons} \):

\[ \text{Daily Oil Consumption (gallons)} = 9.5 \times 10^{6} \times 42 = 399000000 \text{ gallons} \]

Next, we convert the daily oil consumption from gallons to cubic feet using the conversion \( 1 \text{ gallon} = 0.133681 \text{ cubic feet} \):

\[ \text{Daily Oil Consumption (cubic feet)} = 399000000 \times 0.133681 \approx 53338719 \text{ cubic feet} \]

The diameter of the cylindrical tank is given as \( 41 \text{ ft} \), so the radius \( r \) is:

\[ r = \frac{41}{2} = 20.5 \text{ ft} \]

Using the volume formula for a cylinder \( V = \pi r^2 h \), we can solve for the height \( h \):

\[ h = \frac{V}{\pi r^2} = \frac{53338719}{\pi (20.5)^2} \]

Calculating this gives:

\[ h \approx 40400.34 \text{ ft} \]

Final Answer