Answer :
To find the approximate total volume of the grain silo, which consists of a cylindrical portion and a hemispherical portion, follow these steps:
1. Determine the radius of the silo:
- 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]\( V = \pi \times \text{radius}^2 \times \text{height} \)[/tex].
- Plug in the given values (using [tex]\(\pi = 3.14\)[/tex]):
[tex]\( V_{\text{cylinder}} = 3.14 \times (2.2)^2 \times 6.2 \)[/tex].
- Simplifying:
[tex]\( V_{\text{cylinder}} = 94.2 \text{ cubic meters (approximately)} \)[/tex].
3. Calculate the volume of the hemispherical portion:
- The formula for the volume of a hemisphere is:
[tex]\( V = \frac{2}{3} \pi \times \text{radius}^3 \)[/tex].
- Insert the given values:
[tex]\( V_{\text{hemisphere}} = \frac{2}{3} \times 3.14 \times (2.2)^3 \)[/tex].
- Simplifying:
[tex]\( V_{\text{hemisphere}} = 22.3 \text{ cubic meters (approximately)} \)[/tex].
4. Calculate the total volume of the silo:
- Add the volume of the cylindrical portion and the hemispherical portion:
[tex]\( V_{\text{total}} = V_{\text{cylinder}} + V_{\text{hemisphere}} \)[/tex].
- [tex]\( V_{\text{total}} = 94.2 + 22.3 = 116.5 \text{ cubic meters} \)[/tex].
5. Round the total volume:
- The calculated total volume, when rounded to the nearest tenth, is [tex]\(116.5\)[/tex] cubic meters.
Therefore, the approximate total volume of the grain silo is [tex]\(116.5\)[/tex] cubic meters. This corresponds to the answer choice of [tex]\(116.5 \, m^3\)[/tex].
1. Determine the radius of the silo:
- 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]\( V = \pi \times \text{radius}^2 \times \text{height} \)[/tex].
- Plug in the given values (using [tex]\(\pi = 3.14\)[/tex]):
[tex]\( V_{\text{cylinder}} = 3.14 \times (2.2)^2 \times 6.2 \)[/tex].
- Simplifying:
[tex]\( V_{\text{cylinder}} = 94.2 \text{ cubic meters (approximately)} \)[/tex].
3. Calculate the volume of the hemispherical portion:
- The formula for the volume of a hemisphere is:
[tex]\( V = \frac{2}{3} \pi \times \text{radius}^3 \)[/tex].
- Insert the given values:
[tex]\( V_{\text{hemisphere}} = \frac{2}{3} \times 3.14 \times (2.2)^3 \)[/tex].
- Simplifying:
[tex]\( V_{\text{hemisphere}} = 22.3 \text{ cubic meters (approximately)} \)[/tex].
4. Calculate the total volume of the silo:
- Add the volume of the cylindrical portion and the hemispherical portion:
[tex]\( V_{\text{total}} = V_{\text{cylinder}} + V_{\text{hemisphere}} \)[/tex].
- [tex]\( V_{\text{total}} = 94.2 + 22.3 = 116.5 \text{ cubic meters} \)[/tex].
5. Round the total volume:
- The calculated total volume, when rounded to the nearest tenth, is [tex]\(116.5\)[/tex] cubic meters.
Therefore, the approximate total volume of the grain silo is [tex]\(116.5\)[/tex] cubic meters. This corresponds to the answer choice of [tex]\(116.5 \, m^3\)[/tex].
