Answer :
To find the total volume of the grain silo, which is composed of a cylinder and a hemisphere, we need to follow these steps:
1. Determine the radius:
- The diameter of the silo is given as 4.4 meters.
- The radius is half of the diameter, so:
[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.
- Using the provided values:
[tex]\[
V_{\text{cylinder}} = 3.14 \times (2.2)^2 \times 6.2
= 3.14 \times 4.84 \times 6.2
= 94.2 \text{ cubic meters (rounded to the nearest tenth)}
\][/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 have a hemisphere, we take half of this volume:
[tex]\[
V_{\text{hemisphere}} = \frac{1}{2} \times \frac{4}{3} \times 3.14 \times (2.2)^3
= \frac{2}{3} \times 3.14 \times 10.648
= 22.3 \text{ cubic meters (rounded to the nearest tenth)}
\][/tex]
4. Add the volumes of the cylinder and hemisphere to find the total volume:
- Total volume, [tex]\( V_{\text{total}} \)[/tex], is the sum of the cylinder and hemisphere volumes:
[tex]\[
V_{\text{total}} = 94.2 + 22.3 = 116.5 \text{ cubic meters}
\][/tex]
Therefore, the approximate total volume of the silo is [tex]\( \boxed{116.5} \)[/tex] cubic meters.
1. Determine the radius:
- The diameter of the silo is given as 4.4 meters.
- The radius is half of the diameter, so:
[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.
- Using the provided values:
[tex]\[
V_{\text{cylinder}} = 3.14 \times (2.2)^2 \times 6.2
= 3.14 \times 4.84 \times 6.2
= 94.2 \text{ cubic meters (rounded to the nearest tenth)}
\][/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 have a hemisphere, we take half of this volume:
[tex]\[
V_{\text{hemisphere}} = \frac{1}{2} \times \frac{4}{3} \times 3.14 \times (2.2)^3
= \frac{2}{3} \times 3.14 \times 10.648
= 22.3 \text{ cubic meters (rounded to the nearest tenth)}
\][/tex]
4. Add the volumes of the cylinder and hemisphere to find the total volume:
- Total volume, [tex]\( V_{\text{total}} \)[/tex], is the sum of the cylinder and hemisphere volumes:
[tex]\[
V_{\text{total}} = 94.2 + 22.3 = 116.5 \text{ cubic meters}
\][/tex]
Therefore, the approximate total volume of the silo is [tex]\( \boxed{116.5} \)[/tex] cubic meters.
