Answer :
To find the total volume of the silo, which is composed of a cylinder and a hemisphere, we need to calculate the volume of each part separately and then add them together.
1. Find the radius of the silo:
- The diameter of the circular base is 4.4 meters. Therefore, the radius is half of the diameter.
[tex]\[
\text{Radius} = \frac{4.4}{2} = 2.2 \text{ meters}
\][/tex]
2. Calculate the volume of the cylindrical portion:
- The formula for the volume of a cylinder is [tex]\(\pi r^2 h\)[/tex], where [tex]\(r\)[/tex] is the radius and [tex]\(h\)[/tex] is the height.
- The height provided for the cylinder is 6.2 meters.
[tex]\[
\text{Volume of cylinder} = 3.14 \times (2.2)^2 \times 6.2
\][/tex]
3. Calculate the volume of the hemispherical portion:
- The formula for the volume of a sphere is [tex]\(\frac{4}{3} \pi r^3\)[/tex]. Since we have a hemisphere, which is half of a sphere, we use [tex]\(\frac{2}{3} \pi r^3\)[/tex].
[tex]\[
\text{Volume of hemisphere} = \frac{2}{3} \times 3.14 \times (2.2)^3
\][/tex]
4. Add the volumes of the cylinder and the hemisphere to find the total volume of the silo:
[tex]\[
\text{Total Volume} = \text{Volume of cylinder} + \text{Volume of hemisphere}
\][/tex]
5. Round the total volume to the nearest tenth:
Based on these calculations, the approximate total volume of the silo is 116.5 cubic meters.
This matches the option: 116.5 m³.
1. Find the radius of the silo:
- The diameter of the circular base is 4.4 meters. Therefore, the radius is half of the diameter.
[tex]\[
\text{Radius} = \frac{4.4}{2} = 2.2 \text{ meters}
\][/tex]
2. Calculate the volume of the cylindrical portion:
- The formula for the volume of a cylinder is [tex]\(\pi r^2 h\)[/tex], where [tex]\(r\)[/tex] is the radius and [tex]\(h\)[/tex] is the height.
- The height provided for the cylinder is 6.2 meters.
[tex]\[
\text{Volume of cylinder} = 3.14 \times (2.2)^2 \times 6.2
\][/tex]
3. Calculate the volume of the hemispherical portion:
- The formula for the volume of a sphere is [tex]\(\frac{4}{3} \pi r^3\)[/tex]. Since we have a hemisphere, which is half of a sphere, we use [tex]\(\frac{2}{3} \pi r^3\)[/tex].
[tex]\[
\text{Volume of hemisphere} = \frac{2}{3} \times 3.14 \times (2.2)^3
\][/tex]
4. Add the volumes of the cylinder and the hemisphere to find the total volume of the silo:
[tex]\[
\text{Total Volume} = \text{Volume of cylinder} + \text{Volume of hemisphere}
\][/tex]
5. Round the total volume to the nearest tenth:
Based on these calculations, the approximate total volume of the silo is 116.5 cubic meters.
This matches the option: 116.5 m³.
