Answer :
To find the total volume of the grain silo, which is composed of a cylinder and a hemisphere, we need to calculate the volumes of each part separately and then add them together. Here's a step-by-step solution:
1. Identify the Components:
- The silo consists of a cylindrical portion and a hemispherical portion.
- The diameter of both the cylinder and hemisphere is given as 4.4 meters.
2. Find the Radius:
- The radius ([tex]\( r \)[/tex]) is half of the diameter.
[tex]\[
r = \frac{4.4}{2} = 2.2 \text{ meters}
\][/tex]
3. Calculate the Volume of the Cylindrical Portion:
- The formula for the volume of a cylinder is [tex]\( V = \pi r^2 h \)[/tex].
- Height ([tex]\( h \)[/tex]) of the cylindrical portion is 6.2 meters.
[tex]\[
V_{\text{cylinder}} = 3.14 \times (2.2)^2 \times 6.2
\][/tex]
[tex]\[
V_{\text{cylinder}} \approx 94.2 \text{ cubic meters}
\][/tex]
4. 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 it's a hemisphere, we take half of the sphere’s volume: [tex]\( V_{\text{hemisphere}} = \frac{1}{2} \times \frac{4}{3} \pi r^3 \)[/tex].
[tex]\[
V_{\text{hemisphere}} = \frac{2}{3} \times 3.14 \times (2.2)^3
\][/tex]
[tex]\[
V_{\text{hemisphere}} \approx 22.3 \text{ cubic meters}
\][/tex]
5. Add the Volumes:
- Add the volumes of the cylinder and hemisphere to get the total volume.
[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]
6. Round to the Nearest Tenth:
- The total volume of the silo, rounded to the nearest tenth, is approximately 116.5 cubic meters.
Therefore, the approximate total volume of the grain silo is [tex]\( 116.5 \)[/tex] cubic meters.
1. Identify the Components:
- The silo consists of a cylindrical portion and a hemispherical portion.
- The diameter of both the cylinder and hemisphere is given as 4.4 meters.
2. Find the Radius:
- The radius ([tex]\( r \)[/tex]) is half of the diameter.
[tex]\[
r = \frac{4.4}{2} = 2.2 \text{ meters}
\][/tex]
3. Calculate the Volume of the Cylindrical Portion:
- The formula for the volume of a cylinder is [tex]\( V = \pi r^2 h \)[/tex].
- Height ([tex]\( h \)[/tex]) of the cylindrical portion is 6.2 meters.
[tex]\[
V_{\text{cylinder}} = 3.14 \times (2.2)^2 \times 6.2
\][/tex]
[tex]\[
V_{\text{cylinder}} \approx 94.2 \text{ cubic meters}
\][/tex]
4. 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 it's a hemisphere, we take half of the sphere’s volume: [tex]\( V_{\text{hemisphere}} = \frac{1}{2} \times \frac{4}{3} \pi r^3 \)[/tex].
[tex]\[
V_{\text{hemisphere}} = \frac{2}{3} \times 3.14 \times (2.2)^3
\][/tex]
[tex]\[
V_{\text{hemisphere}} \approx 22.3 \text{ cubic meters}
\][/tex]
5. Add the Volumes:
- Add the volumes of the cylinder and hemisphere to get the total volume.
[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]
6. Round to the Nearest Tenth:
- The total volume of the silo, rounded to the nearest tenth, is approximately 116.5 cubic meters.
Therefore, the approximate total volume of the grain silo is [tex]\( 116.5 \)[/tex] cubic meters.
