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 and then sum them up.
### Step 1: Find the radius
Given the diameter is 4.4 meters, the radius is calculated as:
[tex]\[ \text{Radius} = \frac{\text{Diameter}}{2} = \frac{4.4}{2} = 2.2 \text{ meters} \][/tex]
### Step 2: Calculate the volume of the cylinder
The formula for the volume of a cylinder is:
[tex]\[ V_{\text{cylinder}} = \pi r^2 h \][/tex]
where [tex]\( r \)[/tex] is the radius and [tex]\( h \)[/tex] is the height of the cylindrical portion.
Plug in the values:
- [tex]\( \pi = 3.14 \)[/tex]
- [tex]\( r = 2.2 \)[/tex] meters
- [tex]\( h = 6.2 \)[/tex] meters
[tex]\[ V_{\text{cylinder}} = 3.14 \times (2.2)^2 \times 6.2 \][/tex]
### Step 3: Calculate the volume of the hemisphere
The formula for the volume of a hemisphere is:
[tex]\[ V_{\text{hemisphere}} = \frac{2}{3} \pi r^3 \][/tex]
Plug in the values:
- [tex]\( \pi = 3.14 \)[/tex]
- [tex]\( r = 2.2 \)[/tex] meters
[tex]\[ V_{\text{hemisphere}} = \frac{2}{3} \times 3.14 \times (2.2)^3 \][/tex]
### Step 4: Total volume of the silo
Add the volume of the cylinder and the hemisphere to get the total volume:
[tex]\[ V_{\text{total}} = V_{\text{cylinder}} + V_{\text{hemisphere}} \][/tex]
### Step 5: Round to the nearest tenth
After performing the calculations, the total volume comes out to be:
[tex]\[ V_{\text{total}} \approx 116.5 \text{ cubic meters} \][/tex]
So, the approximate total volume of the silo is 116.5 cubic meters. Therefore, the correct answer is [tex]\(116.5 \, m^3\)[/tex].
### Step 1: Find the radius
Given the diameter is 4.4 meters, the radius is calculated as:
[tex]\[ \text{Radius} = \frac{\text{Diameter}}{2} = \frac{4.4}{2} = 2.2 \text{ meters} \][/tex]
### Step 2: Calculate the volume of the cylinder
The formula for the volume of a cylinder is:
[tex]\[ V_{\text{cylinder}} = \pi r^2 h \][/tex]
where [tex]\( r \)[/tex] is the radius and [tex]\( h \)[/tex] is the height of the cylindrical portion.
Plug in the values:
- [tex]\( \pi = 3.14 \)[/tex]
- [tex]\( r = 2.2 \)[/tex] meters
- [tex]\( h = 6.2 \)[/tex] meters
[tex]\[ V_{\text{cylinder}} = 3.14 \times (2.2)^2 \times 6.2 \][/tex]
### Step 3: Calculate the volume of the hemisphere
The formula for the volume of a hemisphere is:
[tex]\[ V_{\text{hemisphere}} = \frac{2}{3} \pi r^3 \][/tex]
Plug in the values:
- [tex]\( \pi = 3.14 \)[/tex]
- [tex]\( r = 2.2 \)[/tex] meters
[tex]\[ V_{\text{hemisphere}} = \frac{2}{3} \times 3.14 \times (2.2)^3 \][/tex]
### Step 4: Total volume of the silo
Add the volume of the cylinder and the hemisphere to get the total volume:
[tex]\[ V_{\text{total}} = V_{\text{cylinder}} + V_{\text{hemisphere}} \][/tex]
### Step 5: Round to the nearest tenth
After performing the calculations, the total volume comes out to be:
[tex]\[ V_{\text{total}} \approx 116.5 \text{ cubic meters} \][/tex]
So, the approximate total volume of the silo is 116.5 cubic meters. Therefore, the correct answer is [tex]\(116.5 \, m^3\)[/tex].
