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Answer :
To find the total volume of the grain silo, which is composed of a cylindrical portion and a hemispherical portion, we can follow these steps:
1. Determine the Radius:
- The diameter of the silo is given as 4.4 meters.
- The radius, which is half of the diameter, is [tex]\( \frac{4.4}{2} = 2.2 \)[/tex] meters.
2. Calculate the Volume of the Cylindrical Portion:
- 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.
- With the radius of 2.2 meters and the height of 6.2 meters, the volume is:
[tex]\[ V_{\text{cylinder}} = 3.14 \times (2.2)^2 \times 6.2 \][/tex]
[tex]\[ V_{\text{cylinder}} = 94.2 \, \text{cubic meters} \text{ (approximately)}. \][/tex]
3. Calculate the Volume of the Hemispherical Portion:
- The formula for the volume of a sphere is [tex]\( V = \frac{4}{3} \pi r^3 \)[/tex]. Since we have a hemisphere (half of a sphere), we multiply by [tex]\(\frac{1}{2}\)[/tex].
- Therefore, the volume of the hemisphere is:
[tex]\[ V_{\text{hemisphere}} = \frac{2}{3} \pi (2.2)^3 \][/tex]
[tex]\[ V_{\text{hemisphere}} = 22.3 \, \text{cubic meters} \text{ (approximately)}. \][/tex]
4. Find the Total Volume of the Silo:
- Add the volumes of the cylindrical and hemispherical portions to find the total volume:
[tex]\[ V_{\text{total}} = V_{\text{cylinder}} + V_{\text{hemisphere}} \][/tex]
[tex]\[ V_{\text{total}} = 94.2 + 22.3 = 116.5 \, \text{cubic meters} \][/tex]
Therefore, the approximate total volume of the silo is 116.5 cubic meters, and the correct answer is [tex]\( \boxed{116.5} \)[/tex] cubic meters.
1. Determine the Radius:
- The diameter of the silo is given as 4.4 meters.
- The radius, which is half of the diameter, is [tex]\( \frac{4.4}{2} = 2.2 \)[/tex] meters.
2. Calculate the Volume of the Cylindrical Portion:
- 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.
- With the radius of 2.2 meters and the height of 6.2 meters, the volume is:
[tex]\[ V_{\text{cylinder}} = 3.14 \times (2.2)^2 \times 6.2 \][/tex]
[tex]\[ V_{\text{cylinder}} = 94.2 \, \text{cubic meters} \text{ (approximately)}. \][/tex]
3. Calculate the Volume of the Hemispherical Portion:
- The formula for the volume of a sphere is [tex]\( V = \frac{4}{3} \pi r^3 \)[/tex]. Since we have a hemisphere (half of a sphere), we multiply by [tex]\(\frac{1}{2}\)[/tex].
- Therefore, the volume of the hemisphere is:
[tex]\[ V_{\text{hemisphere}} = \frac{2}{3} \pi (2.2)^3 \][/tex]
[tex]\[ V_{\text{hemisphere}} = 22.3 \, \text{cubic meters} \text{ (approximately)}. \][/tex]
4. Find the Total Volume of the Silo:
- Add the volumes of the cylindrical and hemispherical portions to find the total volume:
[tex]\[ V_{\text{total}} = V_{\text{cylinder}} + V_{\text{hemisphere}} \][/tex]
[tex]\[ V_{\text{total}} = 94.2 + 22.3 = 116.5 \, \text{cubic meters} \][/tex]
Therefore, the approximate total volume of the silo is 116.5 cubic meters, and the correct answer is [tex]\( \boxed{116.5} \)[/tex] cubic meters.
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