Answer :
To find the total volume of the grain silo, which consists of a cylindrical portion with a hemisphere on top, we need to calculate the volume of each part separately and then add them together. Let's go through this step-by-step.
1. Calculate the Radius of the Silo:
- The diameter of the silo is given as 4.4 meters.
- The radius (r) is half of the diameter.
[tex]\[
r = \frac{4.4}{2} = 2.2 \text{ meters}
\][/tex]
2. Volume of the Cylindrical Portion:
- The formula for the volume of a cylinder is [tex]\( V = \pi \times r^2 \times h \)[/tex], where:
- [tex]\( r \)[/tex] is the radius,
- [tex]\( h \)[/tex] is the height of the cylinder, which is 6.2 meters, and
- [tex]\( \pi \)[/tex] is approximately 3.14.
- Substituting these values into the formula:
[tex]\[
V_{\text{cylinder}} = 3.14 \times (2.2)^2 \times 6.2
\][/tex]
3. Volume of the Hemispherical Portion:
- The formula for the volume of a hemisphere is [tex]\( V = \frac{2}{3} \times \pi \times r^3 \)[/tex].
- Substituting the radius and value of [tex]\(\pi\)[/tex]:
[tex]\[
V_{\text{hemisphere}} = \frac{2}{3} \times 3.14 \times (2.2)^3
\][/tex]
4. Add the Volumes Together:
- [tex]\( V_{\text{total}} = V_{\text{cylinder}} + V_{\text{hemisphere}} \)[/tex]
5. Round the Total Volume:
- Finally, round the calculated total volume to the nearest tenth of a cubic meter.
The approximate total volume of the silo, after rounding, is 116.5 cubic meters. Therefore, the answer is [tex]\(116.5 \, m^3\)[/tex].
1. Calculate the Radius of the Silo:
- The diameter of the silo is given as 4.4 meters.
- The radius (r) is half of the diameter.
[tex]\[
r = \frac{4.4}{2} = 2.2 \text{ meters}
\][/tex]
2. Volume of the Cylindrical Portion:
- The formula for the volume of a cylinder is [tex]\( V = \pi \times r^2 \times h \)[/tex], where:
- [tex]\( r \)[/tex] is the radius,
- [tex]\( h \)[/tex] is the height of the cylinder, which is 6.2 meters, and
- [tex]\( \pi \)[/tex] is approximately 3.14.
- Substituting these values into the formula:
[tex]\[
V_{\text{cylinder}} = 3.14 \times (2.2)^2 \times 6.2
\][/tex]
3. Volume of the Hemispherical Portion:
- The formula for the volume of a hemisphere is [tex]\( V = \frac{2}{3} \times \pi \times r^3 \)[/tex].
- Substituting the radius and value of [tex]\(\pi\)[/tex]:
[tex]\[
V_{\text{hemisphere}} = \frac{2}{3} \times 3.14 \times (2.2)^3
\][/tex]
4. Add the Volumes Together:
- [tex]\( V_{\text{total}} = V_{\text{cylinder}} + V_{\text{hemisphere}} \)[/tex]
5. Round the Total Volume:
- Finally, round the calculated total volume to the nearest tenth of a cubic meter.
The approximate total volume of the silo, after rounding, is 116.5 cubic meters. Therefore, the answer is [tex]\(116.5 \, m^3\)[/tex].
