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Answer :
To find the total volume of the grain silo, which is composed of a cylindrical portion and a hemispherical top, we'll calculate the volume of each part separately and then add them together.
### Step 1: Calculate the Radius
The diameter of the silo is 4.4 meters, so the radius is half of the diameter:
[tex]\[ \text{Radius} = \frac{4.4}{2} = 2.2 \, \text{meters} \][/tex]
### Step 2: Calculate the Volume of the Cylindrical Portion
The formula to calculate the volume of a cylinder is:
[tex]\[ V_{\text{cylinder}} = \pi r^2 h \][/tex]
where [tex]\( r = 2.2 \, \text{meters} \)[/tex] is the radius and [tex]\( h = 6.2 \, \text{meters} \)[/tex] is the height of the cylinder.
Using [tex]\(\pi \approx 3.14\)[/tex]:
[tex]\[ V_{\text{cylinder}} = 3.14 \times (2.2)^2 \times 6.2 \][/tex]
### Step 3: Calculate the Volume of the Hemisphere
The volume of a hemisphere is given by:
[tex]\[ V_{\text{hemisphere}} = \frac{2}{3} \pi r^3 \][/tex]
where [tex]\( r = 2.2 \, \text{meters} \)[/tex].
Using [tex]\(\pi \approx 3.14\)[/tex]:
[tex]\[ V_{\text{hemisphere}} = \frac{2}{3} \times 3.14 \times (2.2)^3 \][/tex]
### Step 4: Calculate the Total Volume of the Silo
Add the volumes of the cylindrical portion and the hemisphere to find the total volume:
[tex]\[ V_{\text{total}} = V_{\text{cylinder}} + V_{\text{hemisphere}} \][/tex]
### Final Result
After performing the calculations, the approximate total volume of the silo is:
[tex]\[ V_{\text{total}} \approx 116.5 \, \text{cubic meters} \][/tex]
Therefore, the answer is:
[tex]\[ \boxed{116.5 \, m^3} \][/tex]
### Step 1: Calculate the Radius
The diameter of the silo is 4.4 meters, so the radius is half of the diameter:
[tex]\[ \text{Radius} = \frac{4.4}{2} = 2.2 \, \text{meters} \][/tex]
### Step 2: Calculate the Volume of the Cylindrical Portion
The formula to calculate the volume of a cylinder is:
[tex]\[ V_{\text{cylinder}} = \pi r^2 h \][/tex]
where [tex]\( r = 2.2 \, \text{meters} \)[/tex] is the radius and [tex]\( h = 6.2 \, \text{meters} \)[/tex] is the height of the cylinder.
Using [tex]\(\pi \approx 3.14\)[/tex]:
[tex]\[ V_{\text{cylinder}} = 3.14 \times (2.2)^2 \times 6.2 \][/tex]
### Step 3: Calculate the Volume of the Hemisphere
The volume of a hemisphere is given by:
[tex]\[ V_{\text{hemisphere}} = \frac{2}{3} \pi r^3 \][/tex]
where [tex]\( r = 2.2 \, \text{meters} \)[/tex].
Using [tex]\(\pi \approx 3.14\)[/tex]:
[tex]\[ V_{\text{hemisphere}} = \frac{2}{3} \times 3.14 \times (2.2)^3 \][/tex]
### Step 4: Calculate the Total Volume of the Silo
Add the volumes of the cylindrical portion and the hemisphere to find the total volume:
[tex]\[ V_{\text{total}} = V_{\text{cylinder}} + V_{\text{hemisphere}} \][/tex]
### Final Result
After performing the calculations, the approximate total volume of the silo is:
[tex]\[ V_{\text{total}} \approx 116.5 \, \text{cubic meters} \][/tex]
Therefore, the answer is:
[tex]\[ \boxed{116.5 \, m^3} \][/tex]
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