Answer :
To find the approximate total volume of the grain silo, which consists of a cylindrical portion and a hemispherical portion, we need to follow these steps:
1. Find the Radius:
- The diameter of the silo is given as 4.4 meters. To find the radius, divide the diameter by 2.
[tex]\[
\text{Radius} = \frac{4.4}{2} = 2.2 \text{ meters}
\][/tex]
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.
- The height of the cylindrical portion is 6.2 meters.
[tex]\[
V_{\text{cylinder}} = 3.14 \times (2.2)^2 \times 6.2
\][/tex]
- Calculate [tex]\( V_{\text{cylinder}} \)[/tex]:
[tex]\[
V_{\text{cylinder}} \approx 94.2 \text{ cubic meters}
\][/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 need the volume of a hemisphere, we'll use half of this formula: [tex]\( V = \frac{1}{2} \times \frac{4}{3} \pi r^3 = \frac{2}{3} \pi r^3 \)[/tex].
[tex]\[
V_{\text{hemisphere}} = \frac{2}{3} \times 3.14 \times (2.2)^3
\][/tex]
- Calculate [tex]\( V_{\text{hemisphere}} \)[/tex]:
[tex]\[
V_{\text{hemisphere}} \approx 22.3 \text{ cubic meters}
\][/tex]
4. Find the Total Volume of the Silo:
- Add the volume of the cylindrical portion and the volume of the hemispherical portion together.
[tex]\[
V_{\text{total}} = V_{\text{cylinder}} + V_{\text{hemisphere}}
\][/tex]
[tex]\[
V_{\text{total}} \approx 94.2 + 22.3 = 116.5 \text{ cubic meters}
\][/tex]
5. Round the Result:
- The total volume is approximately 116.5 cubic meters when rounded to the nearest tenth.
The approximate total volume of the grain silo is 116.5 cubic meters. The correct answer is:
116.5 m³
1. Find the Radius:
- The diameter of the silo is given as 4.4 meters. To find the radius, divide the diameter by 2.
[tex]\[
\text{Radius} = \frac{4.4}{2} = 2.2 \text{ meters}
\][/tex]
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.
- The height of the cylindrical portion is 6.2 meters.
[tex]\[
V_{\text{cylinder}} = 3.14 \times (2.2)^2 \times 6.2
\][/tex]
- Calculate [tex]\( V_{\text{cylinder}} \)[/tex]:
[tex]\[
V_{\text{cylinder}} \approx 94.2 \text{ cubic meters}
\][/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 need the volume of a hemisphere, we'll use half of this formula: [tex]\( V = \frac{1}{2} \times \frac{4}{3} \pi r^3 = \frac{2}{3} \pi r^3 \)[/tex].
[tex]\[
V_{\text{hemisphere}} = \frac{2}{3} \times 3.14 \times (2.2)^3
\][/tex]
- Calculate [tex]\( V_{\text{hemisphere}} \)[/tex]:
[tex]\[
V_{\text{hemisphere}} \approx 22.3 \text{ cubic meters}
\][/tex]
4. Find the Total Volume of the Silo:
- Add the volume of the cylindrical portion and the volume of the hemispherical portion together.
[tex]\[
V_{\text{total}} = V_{\text{cylinder}} + V_{\text{hemisphere}}
\][/tex]
[tex]\[
V_{\text{total}} \approx 94.2 + 22.3 = 116.5 \text{ cubic meters}
\][/tex]
5. Round the Result:
- The total volume is approximately 116.5 cubic meters when rounded to the nearest tenth.
The approximate total volume of the grain silo is 116.5 cubic meters. The correct answer is:
116.5 m³
