Answer :
To find the total volume of the grain silo, which is composed of a cylinder and a hemisphere, follow these steps:
1. Identify the Components and Given Values:
- The silo consists of a cylindrical portion and a hemispherical top.
- Diameter of the silo: 4.4 meters
- Height of the cylinder: 6.2 meters
- Use [tex]\( \pi = 3.14 \)[/tex].
2. Calculate the Radius:
- The radius of the cylindrical and hemispherical portions is half the diameter.
- [tex]\( \text{Radius} = \frac{\text{Diameter}}{2} = \frac{4.4}{2} = 2.2 \)[/tex] meters.
3. Calculate the Volume of the Cylinder:
- The formula for the volume of a cylinder is [tex]\( V = \pi r^2 h \)[/tex], where [tex]\( r \)[/tex] is the radius, and [tex]\( h \)[/tex] is the height.
- Using the values we have:
[tex]\[
V_{\text{cylinder}} = 3.14 \times (2.2)^2 \times 6.2
= 94.2 \text{ cubic meters (rounded slightly from 94.225)}
\][/tex]
4. Calculate the Volume of the Hemisphere:
- The formula for the volume of a hemisphere is [tex]\( V = \frac{2}{3} \pi r^3 \)[/tex].
- Using the given radius:
[tex]\[
V_{\text{hemisphere}} = \frac{2}{3} \times 3.14 \times (2.2)^3
= 22.3 \text{ cubic meters (rounded slightly from 22.29)}
\][/tex]
5. Calculate the Total Volume of the Silo:
- Add the volume of the cylindrical part and the hemispherical part:
[tex]\[
\text{Total Volume} = V_{\text{cylinder}} + V_{\text{hemisphere}} = 94.2 + 22.3 = 116.5 \text{ cubic meters}
\][/tex]
Therefore, the approximate total volume of the silo is 116.5 cubic meters. This matches the answer choice: [tex]\( \boxed{116.5 \, m^3} \)[/tex].
1. Identify the Components and Given Values:
- The silo consists of a cylindrical portion and a hemispherical top.
- Diameter of the silo: 4.4 meters
- Height of the cylinder: 6.2 meters
- Use [tex]\( \pi = 3.14 \)[/tex].
2. Calculate the Radius:
- The radius of the cylindrical and hemispherical portions is half the diameter.
- [tex]\( \text{Radius} = \frac{\text{Diameter}}{2} = \frac{4.4}{2} = 2.2 \)[/tex] meters.
3. Calculate the Volume of the Cylinder:
- The formula for the volume of a cylinder is [tex]\( V = \pi r^2 h \)[/tex], where [tex]\( r \)[/tex] is the radius, and [tex]\( h \)[/tex] is the height.
- Using the values we have:
[tex]\[
V_{\text{cylinder}} = 3.14 \times (2.2)^2 \times 6.2
= 94.2 \text{ cubic meters (rounded slightly from 94.225)}
\][/tex]
4. Calculate the Volume of the Hemisphere:
- The formula for the volume of a hemisphere is [tex]\( V = \frac{2}{3} \pi r^3 \)[/tex].
- Using the given radius:
[tex]\[
V_{\text{hemisphere}} = \frac{2}{3} \times 3.14 \times (2.2)^3
= 22.3 \text{ cubic meters (rounded slightly from 22.29)}
\][/tex]
5. Calculate the Total Volume of the Silo:
- Add the volume of the cylindrical part and the hemispherical part:
[tex]\[
\text{Total Volume} = V_{\text{cylinder}} + V_{\text{hemisphere}} = 94.2 + 22.3 = 116.5 \text{ cubic meters}
\][/tex]
Therefore, the approximate total volume of the silo is 116.5 cubic meters. This matches the answer choice: [tex]\( \boxed{116.5 \, m^3} \)[/tex].
