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Answer :
To find the capacity of the storage tank in gallons, we need to follow these steps:
1. Determine the Dimensions:
- The diameter of the tank is given as 16 feet.
- The height of the tank is 18 feet and 9 inches. Since 9 inches is 9/12 of a foot, we convert this to feet:
[tex]\[
9 \text{ inches} = \frac{9}{12} \text{ feet} = 0.75 \text{ feet}
\][/tex]
- So, the total height of the tank is:
[tex]\[
18 + 0.75 = 18.75 \text{ feet}
\][/tex]
2. Calculate the Radius:
- The radius is half of the diameter. Therefore:
[tex]\[
\text{Radius} = \frac{16}{2} = 8 \text{ feet}
\][/tex]
3. Calculate the Volume in Cubic Feet:
- The formula for the volume of a cylinder is:
[tex]\[
V = \pi \times \text{radius}^2 \times \text{height}
\][/tex]
- Substituting the values we have:
[tex]\[
V = \pi \times 8^2 \times 18.75
\][/tex]
- This results in the volume being approximately:
[tex]\[
3769.91 \text{ cubic feet}
\][/tex]
4. Convert the Volume to Gallons:
- Since one cubic foot contains 7.481 gallons, we multiply the volume in cubic feet by this conversion factor:
[tex]\[
\text{Volume in gallons} = 3769.91 \times 7.481
\][/tex]
- This gives us approximately:
[tex]\[
28202.71 \text{ gallons}
\][/tex]
Thus, the capacity of the storage tank is approximately 28,202.71 gallons.
1. Determine the Dimensions:
- The diameter of the tank is given as 16 feet.
- The height of the tank is 18 feet and 9 inches. Since 9 inches is 9/12 of a foot, we convert this to feet:
[tex]\[
9 \text{ inches} = \frac{9}{12} \text{ feet} = 0.75 \text{ feet}
\][/tex]
- So, the total height of the tank is:
[tex]\[
18 + 0.75 = 18.75 \text{ feet}
\][/tex]
2. Calculate the Radius:
- The radius is half of the diameter. Therefore:
[tex]\[
\text{Radius} = \frac{16}{2} = 8 \text{ feet}
\][/tex]
3. Calculate the Volume in Cubic Feet:
- The formula for the volume of a cylinder is:
[tex]\[
V = \pi \times \text{radius}^2 \times \text{height}
\][/tex]
- Substituting the values we have:
[tex]\[
V = \pi \times 8^2 \times 18.75
\][/tex]
- This results in the volume being approximately:
[tex]\[
3769.91 \text{ cubic feet}
\][/tex]
4. Convert the Volume to Gallons:
- Since one cubic foot contains 7.481 gallons, we multiply the volume in cubic feet by this conversion factor:
[tex]\[
\text{Volume in gallons} = 3769.91 \times 7.481
\][/tex]
- This gives us approximately:
[tex]\[
28202.71 \text{ gallons}
\][/tex]
Thus, the capacity of the storage tank is approximately 28,202.71 gallons.
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