Answer :
To find the total volume of the grain silo, which is composed of a cylindrical portion and a hemispherical portion, we can break down the problem into the following steps:
1. Find the radius of the silo:
- Since the diameter of the silo is 4.4 meters, we can calculate the radius by dividing the diameter by 2.
- Radius = 4.4 meters / 2 = 2.2 meters
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]
- Using the given values, the height of the cylinder is 6.2 meters and [tex]\(\pi = 3.14\)[/tex].
- Volume of the cylinder = [tex]\(3.14 \times (2.2)^2 \times 6.2\)[/tex]
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]
- Using the given value [tex]\(\pi = 3.14\)[/tex].
- Volume of the hemisphere = [tex]\(\frac{2}{3} \times 3.14 \times (2.2)^3\)[/tex]
4. Calculate the total volume of the silo:
- Add the volume of the cylinder to the volume of the hemisphere to find the total volume.
- Total volume = Volume of the cylinder + Volume of the hemisphere
5. Round the total volume to the nearest tenth:
- After calculating, round the total volume to the nearest tenth of a cubic meter.
Based on these calculations, the approximate total volume of the silo is 116.5 cubic meters. So, the final answer is 116.5 m³, which matches the option provided:
[tex]\[ \mathbf{116.5 \, m^3} \][/tex]
1. Find the radius of the silo:
- Since the diameter of the silo is 4.4 meters, we can calculate the radius by dividing the diameter by 2.
- Radius = 4.4 meters / 2 = 2.2 meters
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]
- Using the given values, the height of the cylinder is 6.2 meters and [tex]\(\pi = 3.14\)[/tex].
- Volume of the cylinder = [tex]\(3.14 \times (2.2)^2 \times 6.2\)[/tex]
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]
- Using the given value [tex]\(\pi = 3.14\)[/tex].
- Volume of the hemisphere = [tex]\(\frac{2}{3} \times 3.14 \times (2.2)^3\)[/tex]
4. Calculate the total volume of the silo:
- Add the volume of the cylinder to the volume of the hemisphere to find the total volume.
- Total volume = Volume of the cylinder + Volume of the hemisphere
5. Round the total volume to the nearest tenth:
- After calculating, round the total volume to the nearest tenth of a cubic meter.
Based on these calculations, the approximate total volume of the silo is 116.5 cubic meters. So, the final answer is 116.5 m³, which matches the option provided:
[tex]\[ \mathbf{116.5 \, m^3} \][/tex]
