Answer :
To find the total volume of the grain silo, which is composed of a cylindrical portion and a hemispherical portion on top, we'll calculate the volume for each part separately and then add them together.
### Step 1: Calculate the Volume of the Cylindrical Portion
1. Identify the dimensions of the cylinder:
- Diameter = 4.4 meters.
- Radius = Diameter / 2 = 4.4 / 2 = 2.2 meters.
- Height of the cylinder = 6.2 meters.
2. Use the formula for the volume of a cylinder:
[tex]\[
\text{Volume of the cylinder} = \pi \times (\text{radius}^2) \times \text{height}
\][/tex]
3. Plug in the values:
[tex]\[
\text{Volume of the cylinder} = 3.14 \times (2.2)^2 \times 6.2
\][/tex]
4. Calculate the result:
- Calculate [tex]\((2.2)^2 = 4.84\)[/tex].
- Multiply: [tex]\(3.14 \times 4.84 \times 6.2 \approx 94.2 \text{ cubic meters}\)[/tex].
### Step 2: Calculate the Volume of the Hemispherical Portion
1. Identify the radius of the hemisphere (same as the cylinder's radius):
- Radius = 2.2 meters.
2. Use the formula for the volume of a hemisphere:
[tex]\[
\text{Volume of the hemisphere} = \frac{2}{3} \times \pi \times (\text{radius}^3)
\][/tex]
3. Plug in the values:
[tex]\[
\text{Volume of the hemisphere} = \frac{2}{3} \times 3.14 \times (2.2)^3
\][/tex]
4. Calculate the result:
- Calculate [tex]\((2.2)^3 = 10.648\)[/tex].
- Multiply: [tex]\(\frac{2}{3} \times 3.14 \times 10.648 \approx 22.3 \text{ cubic meters}\)[/tex].
### Step 3: Calculate the Total Volume of the Silo
1. Add the volumes of the cylinder and the hemisphere:
[tex]\[
\text{Total Volume} = 94.2 + 22.3
\][/tex]
2. Calculate the result:
- [tex]\(\text{Total Volume} = 116.5 \text{ cubic meters}\)[/tex].
Therefore, the approximate total volume of the silo is 116.5 cubic meters.
### Step 1: Calculate the Volume of the Cylindrical Portion
1. Identify the dimensions of the cylinder:
- Diameter = 4.4 meters.
- Radius = Diameter / 2 = 4.4 / 2 = 2.2 meters.
- Height of the cylinder = 6.2 meters.
2. Use the formula for the volume of a cylinder:
[tex]\[
\text{Volume of the cylinder} = \pi \times (\text{radius}^2) \times \text{height}
\][/tex]
3. Plug in the values:
[tex]\[
\text{Volume of the cylinder} = 3.14 \times (2.2)^2 \times 6.2
\][/tex]
4. Calculate the result:
- Calculate [tex]\((2.2)^2 = 4.84\)[/tex].
- Multiply: [tex]\(3.14 \times 4.84 \times 6.2 \approx 94.2 \text{ cubic meters}\)[/tex].
### Step 2: Calculate the Volume of the Hemispherical Portion
1. Identify the radius of the hemisphere (same as the cylinder's radius):
- Radius = 2.2 meters.
2. Use the formula for the volume of a hemisphere:
[tex]\[
\text{Volume of the hemisphere} = \frac{2}{3} \times \pi \times (\text{radius}^3)
\][/tex]
3. Plug in the values:
[tex]\[
\text{Volume of the hemisphere} = \frac{2}{3} \times 3.14 \times (2.2)^3
\][/tex]
4. Calculate the result:
- Calculate [tex]\((2.2)^3 = 10.648\)[/tex].
- Multiply: [tex]\(\frac{2}{3} \times 3.14 \times 10.648 \approx 22.3 \text{ cubic meters}\)[/tex].
### Step 3: Calculate the Total Volume of the Silo
1. Add the volumes of the cylinder and the hemisphere:
[tex]\[
\text{Total Volume} = 94.2 + 22.3
\][/tex]
2. Calculate the result:
- [tex]\(\text{Total Volume} = 116.5 \text{ cubic meters}\)[/tex].
Therefore, the approximate total volume of the silo is 116.5 cubic meters.
