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Answer :
To find the total volume of the grain silo, we need to calculate the volume of both the cylindrical portion and the hemispherical portion.
### Step 1: Calculate the volume of the cylindrical portion
- Diameter of the silo: 4.4 meters, so the radius [tex]\( r \)[/tex] is half of the diameter, which is [tex]\( 2.2 \)[/tex] meters.
- Height of the cylindrical portion: 6.2 meters.
- Formula for the volume of a cylinder:
[tex]\[
V_{\text{cylinder}} = \pi \times r^2 \times h
\][/tex]
Using [tex]\( \pi = 3.14 \)[/tex]:
[tex]\[
V_{\text{cylinder}} = 3.14 \times (2.2)^2 \times 6.2
\][/tex]
### Step 2: Calculate the volume of the hemispherical portion
- Formula for the volume of a hemisphere:
[tex]\[
V_{\text{hemisphere}} = \frac{2}{3} \times \pi \times r^3
\][/tex]
Using [tex]\( \pi = 3.14 \)[/tex]:
[tex]\[
V_{\text{hemisphere}} = \frac{2}{3} \times 3.14 \times (2.2)^3
\][/tex]
### Step 3: Calculate the total volume of the silo
- Total volume: The sum of the volumes of the cylindrical and hemispherical portions.
[tex]\[
V_{\text{total}} = V_{\text{cylinder}} + V_{\text{hemisphere}}
\][/tex]
After performing the calculations, we find that the approximate total volume of the silo is [tex]\( 116.5 \)[/tex] cubic meters, rounded to the nearest tenth.
### Step 1: Calculate the volume of the cylindrical portion
- Diameter of the silo: 4.4 meters, so the radius [tex]\( r \)[/tex] is half of the diameter, which is [tex]\( 2.2 \)[/tex] meters.
- Height of the cylindrical portion: 6.2 meters.
- Formula for the volume of a cylinder:
[tex]\[
V_{\text{cylinder}} = \pi \times r^2 \times h
\][/tex]
Using [tex]\( \pi = 3.14 \)[/tex]:
[tex]\[
V_{\text{cylinder}} = 3.14 \times (2.2)^2 \times 6.2
\][/tex]
### Step 2: Calculate the volume of the hemispherical portion
- Formula for the volume of a hemisphere:
[tex]\[
V_{\text{hemisphere}} = \frac{2}{3} \times \pi \times r^3
\][/tex]
Using [tex]\( \pi = 3.14 \)[/tex]:
[tex]\[
V_{\text{hemisphere}} = \frac{2}{3} \times 3.14 \times (2.2)^3
\][/tex]
### Step 3: Calculate the total volume of the silo
- Total volume: The sum of the volumes of the cylindrical and hemispherical portions.
[tex]\[
V_{\text{total}} = V_{\text{cylinder}} + V_{\text{hemisphere}}
\][/tex]
After performing the calculations, we find that the approximate total volume of the silo is [tex]\( 116.5 \)[/tex] cubic meters, rounded to the nearest tenth.
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