Answer :
To find the total volume of the grain silo, which is composed of a cylinder and a hemisphere, follow these steps:
1. Determine the dimensions:
- Diameter of the silo: 4.4 meters
- Radius (half of the diameter):
[tex]\[
\text{Radius} = \frac{4.4}{2} = 2.2 \text{ meters}
\][/tex]
- Height of the cylindrical portion: 6.2 meters
- Use [tex]\(\pi \approx 3.14\)[/tex]
2. Calculate the volume of the cylindrical portion:
- The formula for the volume of a cylinder is:
[tex]\[
\text{Volume of cylinder} = \pi \times \text{radius}^2 \times \text{height}
\][/tex]
- Plug in the values:
[tex]\[
\text{Volume of cylinder} = 3.14 \times (2.2)^2 \times 6.2
\][/tex]
- This calculates to approximately 94.2 cubic meters.
3. Calculate the volume of the hemispherical portion:
- The formula for the volume of a hemisphere is:
[tex]\[
\text{Volume of hemisphere} = \frac{2}{3} \times \pi \times \text{radius}^3
\][/tex]
- Plug in the values:
[tex]\[
\text{Volume of hemisphere} = \frac{2}{3} \times 3.14 \times (2.2)^3
\][/tex]
- This calculates to approximately 22.3 cubic meters.
4. Calculate the total volume of the silo:
- Add the volume of the cylinder and the volume of the hemisphere:
[tex]\[
\text{Total volume} = 94.2 + 22.3
\][/tex]
- This results in approximately 116.5 cubic meters.
5. Round the total volume to the nearest tenth:
- The approximate total volume of the silo is 116.5 cubic meters.
Therefore, the total volume of the silo is approximately 116.5 cubic meters, which matches the answer choice: [tex]\( 116.5 \, m^3 \)[/tex].
1. Determine the dimensions:
- Diameter of the silo: 4.4 meters
- Radius (half of the diameter):
[tex]\[
\text{Radius} = \frac{4.4}{2} = 2.2 \text{ meters}
\][/tex]
- Height of the cylindrical portion: 6.2 meters
- Use [tex]\(\pi \approx 3.14\)[/tex]
2. Calculate the volume of the cylindrical portion:
- The formula for the volume of a cylinder is:
[tex]\[
\text{Volume of cylinder} = \pi \times \text{radius}^2 \times \text{height}
\][/tex]
- Plug in the values:
[tex]\[
\text{Volume of cylinder} = 3.14 \times (2.2)^2 \times 6.2
\][/tex]
- This calculates to approximately 94.2 cubic meters.
3. Calculate the volume of the hemispherical portion:
- The formula for the volume of a hemisphere is:
[tex]\[
\text{Volume of hemisphere} = \frac{2}{3} \times \pi \times \text{radius}^3
\][/tex]
- Plug in the values:
[tex]\[
\text{Volume of hemisphere} = \frac{2}{3} \times 3.14 \times (2.2)^3
\][/tex]
- This calculates to approximately 22.3 cubic meters.
4. Calculate the total volume of the silo:
- Add the volume of the cylinder and the volume of the hemisphere:
[tex]\[
\text{Total volume} = 94.2 + 22.3
\][/tex]
- This results in approximately 116.5 cubic meters.
5. Round the total volume to the nearest tenth:
- The approximate total volume of the silo is 116.5 cubic meters.
Therefore, the total volume of the silo is approximately 116.5 cubic meters, which matches the answer choice: [tex]\( 116.5 \, m^3 \)[/tex].
