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Answer :
To find the total volume of the grain silo, we need to calculate the volumes of both the cylindrical and hemispherical parts, and then add them together. Here are the steps to find the solution:
1. Identify the Known Values:
- Diameter of the silo = 4.4 meters.
- Height of the cylindrical portion = 6.2 meters.
- Use [tex]\( \pi = 3.14 \)[/tex].
2. Calculate the Radius:
Since the diameter is given, we can find the radius by dividing the diameter by 2.
- [tex]\[
\text{Radius} = \frac{\text{Diameter}}{2} = \frac{4.4}{2} = 2.2 \text{ meters}
\][/tex]
3. Calculate the Volume of the Cylinder:
The formula for the volume of a cylinder is:
[tex]\[
V_{\text{cylinder}} = \pi \times \text{radius}^2 \times \text{height}
\][/tex]
- [tex]\[
V_{\text{cylinder}} = 3.14 \times (2.2)^2 \times 6.2 = 94.2 \text{ cubic meters} \text{ (rounded to one decimal place)}
\][/tex]
4. Calculate the Volume of the Hemisphere:
The formula for the volume of a hemisphere is:
[tex]\[
V_{\text{hemisphere}} = \frac{2}{3} \times \pi \times \text{radius}^3
\][/tex]
- [tex]\[
V_{\text{hemisphere}} = \frac{2}{3} \times 3.14 \times (2.2)^3 = 22.3 \text{ cubic meters} \text{ (rounded to one decimal place)}
\][/tex]
5. Calculate the Total Volume of the Silo:
Add the volumes of the cylinder and the hemisphere to find the total volume:
- [tex]\[
V_{\text{total}} = V_{\text{cylinder}} + V_{\text{hemisphere}} = 94.2 + 22.3 = 116.5 \text{ cubic meters}
\][/tex]
After rounding to the nearest tenth of a cubic meter, the approximate total volume of the silo is 116.5 cubic meters.
Thus, the correct answer is: [tex]\( \boxed{116.5} \)[/tex] m³.
1. Identify the Known Values:
- Diameter of the silo = 4.4 meters.
- Height of the cylindrical portion = 6.2 meters.
- Use [tex]\( \pi = 3.14 \)[/tex].
2. Calculate the Radius:
Since the diameter is given, we can find the radius by dividing the diameter by 2.
- [tex]\[
\text{Radius} = \frac{\text{Diameter}}{2} = \frac{4.4}{2} = 2.2 \text{ meters}
\][/tex]
3. Calculate the Volume of the Cylinder:
The formula for the volume of a cylinder is:
[tex]\[
V_{\text{cylinder}} = \pi \times \text{radius}^2 \times \text{height}
\][/tex]
- [tex]\[
V_{\text{cylinder}} = 3.14 \times (2.2)^2 \times 6.2 = 94.2 \text{ cubic meters} \text{ (rounded to one decimal place)}
\][/tex]
4. Calculate the Volume of the Hemisphere:
The formula for the volume of a hemisphere is:
[tex]\[
V_{\text{hemisphere}} = \frac{2}{3} \times \pi \times \text{radius}^3
\][/tex]
- [tex]\[
V_{\text{hemisphere}} = \frac{2}{3} \times 3.14 \times (2.2)^3 = 22.3 \text{ cubic meters} \text{ (rounded to one decimal place)}
\][/tex]
5. Calculate the Total Volume of the Silo:
Add the volumes of the cylinder and the hemisphere to find the total volume:
- [tex]\[
V_{\text{total}} = V_{\text{cylinder}} + V_{\text{hemisphere}} = 94.2 + 22.3 = 116.5 \text{ cubic meters}
\][/tex]
After rounding to the nearest tenth of a cubic meter, the approximate total volume of the silo is 116.5 cubic meters.
Thus, the correct answer is: [tex]\( \boxed{116.5} \)[/tex] m³.
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